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##### Strayer Mat540 full course (Alll assignments +problems+discussions+quiz+midterm +final)

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Question;MAT540;Week;1 Homework;Chapter 1;2. The;Retread Tire Company recaps tires. The fixed annual cost of the recapping;operation is $60,000.The variable cost of recapping a tire is $9.The company;charges $25 to recap a tire.;a. For an annual volume of 12,000 tires, determine;the total cost, total revenue, and profit.;b. Determine the annual break-even volume for the;Retread Tire Company operation.;4. Evergreen;Fertilizer Company produces fertilizer. The company?s fixed monthly cost is;$25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen;sells the fertilizer for $0.40 per pound. Determine the monthly break-even;volume for the company.;12. If;Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer;from $0.40 per pound to $0.60 per pound, what effect will the change have on;the break-even volume?;14. If;Evergreen Fertilizer Company increases its advertising expenditures by $14,000;per year, what effect will the increase have on the break-even volume computed;in Problem 13?;Reference Problem;13: If Evergreen Fertilizer Company changes its;production process to add a weed killer to the fertilizer in order to increase;sales, the variable cost per pound will increase from $0.15 to $0.22. What;effect will this change have on the break-even volume computed in Problem 12?;20. Annie;McCoy, a student at Tech, plans to open a hot dog stand inside Tech?s football;stadium during home games. There are seven home games scheduled for the;upcoming season. She must pay the Tech athletic department a vendor?s fee of;$3,000 for the season. Her stand and other equipment will cost her $4,500 for;the season. She estimates that each hot dog she sells will cost her $0.35. She;has talked to friends at other universities who sell hot dogs at games. Based;on their information and the athletic department?s forecast that each game will;sell out, she anticipates that she will sell approximately 2,000 hot dogs;during each game.;a. What price should she charge for a hot dog in order to break even?;b. What factors might occur during the season that would alter the volume;sold and thus the break-even price Annie might charge?;22. The College of Business at Tech is planning;to begin an online MBA program. The initial start-up cost for computing equipment;facilities, course development, and staff recruitment and development is;$350,000.The college plans to charge tuition of $18,000 per student per year. However;the university administration will charge the college $12,000 per student for;the first 100 students enrolled each year for administrative costs and its;share of the tuition payments.;a. How many students does the college need to enroll in the first year to;break even?;b. If the college can enroll 75 students the first year, how much profit will;it make?;c. The college believes it can increase tuition to $24,000, but doing so;would reduce enrollment to 35. Should;the college consider doing this?;Chapter 11;18. The;following probabilities for grades in management science have been determined;based on past records;Grade;Probability;A;0.10;B;0.30;C;0.40;D;0.10;F;0.10;1.00;The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and;so on. Determine the expected grade and variance for the course.;20. An investment;firm is considering two alternative investments, A and B, under two possible;future sets of economic conditions, good and poor. There is a.60 probability;of good economic conditions occurring and a.40 probability of poor economic;conditions occurring. The expected gains and losses under each economic type of;conditions are shown in the following table;Economic Conditions;Investment;Good;Poor;A;$900,000;-$800,000;B;120,000;70,000;Using the expected value of each investment alternative, determine which;should be selected.;26. The;weight of bags of fertilizer is normally distributed, with a mean of 50 pounds;and a standard deviation of 6 pounds. What is the probability that a bag of;fertilizer will weigh between 45 and 55 pounds?;28. The;Polo Development Firm is building a shopping center. It has informed renters;that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping;center is completed is estimated to be 14 months, with a standard deviation of;4 months, what is the probability that the renters will not be able to occupy;in 19 months?;30. The;manager of the local National Video Store sells videocassette recorders at;discount prices. If the store does not have a video recorder in stock when a;customer wants to buy one, it will lose the sale because the customer will;purchase a recorder from one of the many local competitors. The problem is that;the cost of renting warehouse space to keep enough recorders in inventory to;meet all demand is excessively high. The manager has determined that if 90% of;customer demand for recorders can be met, then the combined cost of lost sales;and inventory will be minimized. The manager has estimated that monthly demand;for recorders is normally distributed, with a mean of 180 recorders and a;standard deviation of 60. Determine the number of recorders the manager should;order each month to meet 90% of customer demand.week 2Click the link above to submit your homework.Complete the following problems from Chapter 12:Problems 8, 16, 24, 32, 36Refer to the tree diagram below to complete problem 36:MAT540;Week 2 Homework;Chapter 12;8. A;local real estate investor in Orlando is considering three alternative;investments: a motel, a restaurant, or a theater. Profits from the motel or;restaurant will be affected by the availability of gasoline and the number of;tourists, profits from the theater will be relatively stable under any;conditions. The following payoff table shows the profit or loss that could;result from each investment;Gasoline Availability;Investment;Shortage;Stable Supply;Surplus;Motel;$-8,000;$15,000;$20,000;Restaurant;2,000;8,000;6,000;Theater;6,000;6,000;5,000;Determine the best investment, using the following decision criteria.;a.;Maximax;b.;Maximin;c.;Minimax regret;d.;Hurwicz (? = 0.4);e. Equal likelihood;16. A concessions;manager at the Tech versus A&M football game must decide whether to have;the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15%;chance of overcast skies, and a 55% chance of sunshine, according to the;weather forecast in College Junction, where the game is to be held. The manager;estimates that the following profits will result from each decision, given each;set of weather conditions;Weather Conditions;Decision;Rain;Overcast;Sunshine;.30;.15;.55;Sun visors;$-500;$-200;$1,500;Umbrellas;2,000;0;-900;a.;Compute the expected value for each decision and select the best one.;b. Develop the opportunity loss;table and compute the expected opportunity loss for each decision.;24. In;Problem 13 the Place-Plus real estate development firm has hired an economist;to assign a probability to each direction interest rates may take over the next;5 years. The economist has determined that there is a.50 probability that;interest rates will decline, a.40 probability that rates will remain stable, and;a.10 probability that rates will increase.;a.;Using expected value, determine the best project.;b.;Determine the expected value of perfect information.;Reference Problem 13: Place-Plus;a real estate development firm, is considering several alternative development;projects. These include building and;leasing an office park, purchasing a parcel of land and building an office building;to rent, buying and leasing a warehouse, building a strip mall, and building;and selling condominiums. The financial success of these projects depends on;interest rate movement in the next 5 years. The various development projects;and their 5-year financial return (in $1,000,000s) given that interest rates;will decline, remain stable, or increase, are shown in the following payoff;table;Interest Rate;Project;Decline;Stable;Increase;Office park;$0.5;$1.7;$4.5;Office building;1.5;1.9;2.5;Warehouse;1.7;1.4;1.0;Mall;0.7;2.4;3.6;Condominiums;3.2;1.5;0.6;32. The;director of career advising at Orange Community College wants to use decision;analysis to provide information to help students decide which 2-year degree;program they should pursue. The director has set up the following payoff table;for six of the most popular and successful degree programs at OCC that shows;the estimated 5-year gross income ($) from each degree for four future economic;conditions;Economic;Conditions;Degree Program;Recession;Average;Good;Robust;Graphic design;145,000;175,000;220,000;260,000;Nursing;150,000;180,000;205,000;215,000;Real estate;115,000;165,000;220,000;320,000;Medical technology;130,000;180,000;210,000;280,000;Culinary technology;115,000;145,000;235,000;305,000;Computer information;technology;125,000;150,000;190,000;250,000;Determine the best degree program in terms of projected income, using the;following decision criteria;a.;Maximax;b.;Maximin;c.;Equal likelihood;d.;Hurwicz (? = 0.50);36. Construct;a decision tree for the decision situation described in Problem 25 and indicate;the best decision.;Reference Problem;25: Fenton and Farrah Friendly, husband-and-wife;car dealers, are soon going to open a new dealership. They have three offers;from a foreign compact car company, from a U.S. producer of full-sized cars, and;from a truck company. The success of each type of dealership will depend on how;much gasoline is going to be available during the next few years. The profit;from each type of dealership, given the availability of gas, is shown in the;following payoff table;Gasoline Availability;Dealership;Shortage;Surplus;.6;.4;Compact cars;$ 300,000;$150,000;Full-sized cars;-100,000;600,000;Trucks;120,000;170,000;Decision Tree diagram to complete:MAT540;Week;3 Homework;Chapter 14;1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3;4, 5, or 6 hours, according to the following probability distribution. The;squad is on duty 24 hours per day, 7 days per week;Time Between;Emergency Calls (hr.);Probability;1;0.05;2;0.10;3;0.30;4;0.30;5;0.20;6;0.05;1.00;a.;Simulate the emergency calls for 3 days (note that this will require a;?running?, or cumulative, hourly clock), using the random number table.;b.;Compute the average time between calls and compare this value with the;expected value of the time between calls from the probability distribution. Why;are the results different?;2. The time between arrivals of cars at the Petroco Service Station;is defined by the following probability distribution;Time Between;Arrivals (min.);Probability;1;0.15;2;0.30;3;0.40;4;0.15;1.00;a.;Simulate the arrival of cars at the service station for 20 arrivals and;compute the average time between arrivals.;b.;Simulate the arrival of cars at the service station for 1 hour, using a;different stream of random numbers from those used in (a) and compute the;average time between arrivals.;c.;Compare the results obtained in (a) and (b).;3. The Dynaco Manufacturing Company produces a product in a process;consisting of operations of five machines. The probability distribution of the;number of machines that will break down in a week follows;Machine Breakdowns;per Week;Probability;0;0.10;1;0.10;2;0.20;3;0.25;4;0.30;5;0.05;1.00;a.;Simulate the machine breakdowns per week for 20 weeks.;b.;Compute the average number of machines that will break down per week.;5. Simulate the decision situation described in Problem 16(a) at the;end of Chapter 12 for 20 weeks, and recommend the best decision.;Reference Problem 16(a) in Chapter 12: A concessions manager at the Tech versus;A&M football game must decide whether to have the vendors sell sun visors;or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and;a 55% chance of sunshine, according to the weather forecast in College;Junction, where the game is to be held. The manager estimates that the;following profits will result from each decision, given each set of weather;conditions;Weather Conditions;Decision;Rain;Overcast;Sunshine;.30;.15;.55;Sun visors;$-500;$-200;$1,500;Umbrellas;2,000;0;-900;a. Compute the expected value;for each decision and select the best one.;6. Every time a machine breaks down at the;Dynaco Manufacturing Company (Problem 3), either 1, 2, or 3 hours are required;to fix it, according to the following probability distribution;Repair Time (hr.);Probability;1;0.30;2;0.50;3;0.20;1.00;a.;Simulate the repair time for 20 weeks and then compute the average weekly;repair time.MAT540;Week;6 Homework;Chapter 2;2.;A company produces two products that are processed on two assembly;lines. Assembly line 1 has 100 available;hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing;time on line 1, while on line 2 product 1 requires 7 hours and product 2;requires 3 hours. The profit for product;1 is $6 per unit, and the profit for product 2 is $4 per unit.;a.;Formulate a linear programming model for this problem.;b.;Solve the model by using graphical analysis.;6.;The Pinewood Furniture Company produces chairs and tables from two;resources ? labor and wood. The company;has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per;day. Each chair requires 8 hours of;labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6;board-ft. of wood. The profit derived;from each chair is $400 and from each table, $100. The company wants to determine the number of;chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this;problem.;a.;Formulate a linear programming model for this problem.;b.;Solve the model by using graphical analysis.;7.;In Problem 6, how much labor and wood will be unused if the optimal numbers;of chairs and tables are produced?;12.;The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three;antibiotics, in different proportions.;One gram of ingredient 1 contributes 3 units and one gram of ingredient;2 contributes 1 unit of antibiotic 1, the drug requires 6 units. At least 4 units of antibiotic 2 are required;and the ingredients contribute 1 unit each per gram. At least 12 units of antibiotic 3 are;required, a gram of ingredient 1 contributes 2 units, and a gram of ingredient;2 contributes 6 units. The cost for a;gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is;$50. The company wants to formulate a;linear programming model to determine the number of grams of each ingredient;that must go into the drug in order to meet the antibiotic requirements at the;minimum cost.;a.;Formulate a linear programming model for this problem.;b.;Solve the model by using graphical analysis.;16.;A clothier makes coats and;slacks. The two resources required are;wool cloth and labor. The clothier has;150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and;10 hours of labor, whereas each pair of slacks requires 5 square yards of wool;and 4 hours of labor. The profit for a;coat is $50, and the profit for slacks is $40.;The clothier wants to determine the number of coats and pairs of slacks;to make so that profit will be maximized.;a.;Formulate a linear programming model for this problem.;b. Solve the model by using;graphical analysis.;20.;Solve the following linear programming model graphically;Maximize Z = 5x1;+ 8x2;Subject to;3x1 + 5x2? 50;2x1 + 4x2? 40;x1? 8;x2? 10;x1, x2? 0MAT540;Week;7 Homework;Chapter 3;8.;Solve the model formulated in Problem 7 for Southern Sporting Goods Company;using the computer.;a.;State the optimal solution.;b.;What would be the effect on the optimal solution if the profit for a;basketball changed from $12 to $13? What;would be the effect if the profit for a football changed from $16 to $15?;c. What would be the effect on;the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional;square feet of leather could be obtained?;Reference Problem 7. Southern;Sporting Good Company makes basketballs and footballs. Each product is produced from two resources;rubber and leather. The resource;requirements for each product and the total resources available are as follows;Resource Requirements per;Unit;Product;Rubber (lb.);Leather (ft2);Basketball;3;4;Football;2;5;Total resources available;500 lb.;800 ft2;10.;A company produces two products, A and B, which have profits of $9 and $7;respectively. Each unit of product must;be processed on two assembly lines, where the required production times are as;follows;Hours/ Unit;Product;Line 1;Line2;A;12;4;B;4;8;Total Hours;60;40;a.;Formulate a linear programming model to determine the optimal product mix that;will maximize profit.;b.;Transform this model into standard form.;11.;Solve problem 10 using the computer.;a.;State the optimal solution.;b.;What would be the effect on the optimal solution if the production time on;line 1 was reduced to 40 hours?;c.;What would be the effect on the optimal solution if the profit for product;B was increased from $7 to $15 to $20?;12.;For the linear programming model formulated in Problem 10 and solved in;Problem 11.;a.;What are the sensitivity ranges for the objective function coefficients?;b.;Determine the shadow prices for additional hours of production time on line;1 and line 2 and indicate whether the company would prefer additional line 1 or;line 2 hours.;14.;Solve the model formulated in Problem 13 for Irwin Textile Mills.;a.;How much extra cotton and processing;time are left over at the optimal solution?;Is the demand for corduroy met?;b.;What is the effect on the optimal solution if the profit per yard of denim;is increased from $2.25 to $3.00? What;is the effect if the profit per yard of corduroy is increased from $3.10 to;$4.00?;c.;What would be the effect on the optimal solution if Irwin Mils could obtain;only 6,000 pounds of cotton per month?;Reference Problem 13. Irwin;Textile Mills produces two types of cotton cloth ? denim and corduroy. Corduroy is a heavier grade of cotton cloth;and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim;requires 5 pounds of raw cotton per yard.;A yard of corduroy requires 3.2 hours of processing time, a yard of;denim requires 3.0 hours. Although the;demand for denim is practically unlimited, the maximum demand for corduroy is;510 yards per month. The manufacturer;has 6,500 pounds of cotton and 3,000 hours of processing time available each;month. The manufacturer makes a profit;of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards;of each type of cloth to produce to maximize profit. Formulate the model and put it into standard;form. Solve it.;15.;Continuing the model from Problem 14.;a.;If Irwin Mills can obtain additional cotton or processing time, but not;both, which should it select? How;much? Explain your answer.;b.;Identify the sensitivity ranges for the objective function coefficients and;for the constraint quantity values. Then;explain the sensitivity range for the demand for corduroy.;16.;United Aluminum Company of Cincinnati produces three grades (high, medium;and low) of aluminum at two mills. Each mill;has a different production capacity (in tons per day) for each grade as;follows;Aluminum Grade;Mill;1;2;High;6;2;Medium;2;2;Low;4;10;The company has contracted;with a manufacturing firm to supply at least 12 tons of high-grade aluminum;and 5 tons of low-grade aluminum. It;costs United $6,000 per day to operate mill 1 and $7,000 per day to operate;mill 2. The company wants to know the;number of days to operate each mill in order to meet the contract at minimum;cost.;a. Formulate a linear;programming model for this problem.;18.;Solve the linear programming model formulated in Problem 16 for Unite;Aluminum Company by using the computer.;a.;Identify and explain the shadow prices for each of the aluminum grade;contract requirements.;b.;Identify the sensitivity ranges for the objective function coefficients and;the constraint quantity values.;c.;Would the solution values change if the contract requirements for;high-grade alumimum were increased from 12 tons to 20 tons? If yes, what would the new solution values;be?;24.;Solve the linear programming model developed in Problem 22 for the Burger;Doodle restaurant by using the computer.;a.;Identify and explain the shadow prices for each of the resource constraints;b.;Which of the resources constrains profit the most?;c.;Identify the sensitivity ranges for the profit of a sausage biscuit and the;amount of sausage available. Explain;these sensitivity ranges.;Reference Problem 22. The;manager of a Burger Doodle franchise wants to determine how many sausage;biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the;following resources;Biscuit;Labor (hr.);Sausage (lb.);Ham (lb.);Flour (lb.);Sausage;0.010;0.10;---;0.04;Ham;0.024;---;0.15;0.04;The franchise has 6 hours of labor available each morning. The manager has a contract with a local;grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of;flour. The profit for a sausage biscuit;is $0.60, the profit for a ham biscuit is $0.50. The manager wants to know the number of each;type of biscuit to prepare each morning in order to maximize profit. Formulate a linear programming model for this;problem. MAT540;Week;8 Homework;Chapter 4;14.;Grafton Metalworks Company produces metal alloys from six different ores it;mines. The company has an order from a;customer to produce an alloy that contains four metals according to the;following specifications: at least 21%;of metal A, no more than 12% of metal B, no more than 7% of metal C and between;30% and 65% of metal D. The proportion;of the four metals in each of the six ores and the level of impurities in each;ore are provided in the following table;Ore;Metal (%);Impurities (%);Cost/Ton;A;B;C;D;1;19;15;12;14;40;27;2;43;10;25;7;15;25;3;17;0;0;53;30;32;4;20;12;0;18;50;22;5;0;24;10;31;35;20;6;12;18;16;25;29;24;When the metals are processed and refined, the;impurities are removed.;The company wants to know the amount of each ore;to use per ton of the alloy that will minimize the cost per ton of the alloy.;a.;Formulate a linear programming model;for this problem.;b.;Solve the model by using the computer.;19.;As a result of a recently passed bill, a congressman?s district has been;allocated $4 million for programs and projects.;It is up to the congressman to decide how to distribute the money. The congressman has decided to allocate the;money to four ongoing programs because of their importance to his district ? a;job training program, a parks project, a sanitation project, and a mobile;library. However, the congressman wants;to distribute the money in a manner that will please the most voters, or, in;other words, gain him the most votes in the upcoming election. His staff?s estimates of the number of votes;gained per dollar spent for the various programs are as follows.;Program;Votes/ Dollar;Job training;0.02;Parks;0.09;Sanitation;0.06;Mobile library;0.04;In order also to satisfy several local influential citizens who financed;his election, he is obligated to observe the following guidelines;?;None of the programs can receive more than 40% of the total allocation.;?;The amount allocated to parks cannot exceed the total allocated to both the;sanitation project and the mobile library;?;The amount allocated to job training must at least equal the amount spent;on the sanitation project.;Any money not spent in the district will be returned to the government;therefore, the congressman wants to spend it all. The congressman wants to know the amount to;allocate to each program to maximize his votes.;a.;Formulate a linear programming model for this problem.;b. Solve the model by using the;computer.;20.;Anna Broderick is the dietician for the State University football team, and;she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional;guidelines for each lunch serving;?;Between 1,500 and 2,000 calories;?;At least 5 mg of iron;?;At least 20 but no more than 60 g of fat;?;At least 30 g of protein;?;At least 40 g of carbohydrates;?;No more than 30 mg of cholesterol;She selects the menu from seven basic food items, as follows, with the;nutritional contributions per pound and the cost as given;Calories;(per lb.);Iron;(mg/lb.);Protein;(g/lb.);Carbo-hydrates;(g/lb.);Fat (g/lb.);Chol-esterol;(mg/lb.);Cost;$/lb.;Chicken;520;4.4;17;0;30;180;0.80;Fish;500;3.3;85;0;5;90;3.70;Ground beef;860;0.3;82;0;75;350;2.30;Dried beans;600;3.4;10;30;3;0;0.90;Lettuce;50;0.5;6;0;0;0;0.75;Potatoes;460;2.2;10;70;0;0;0.40;Milk (2%);240;0.2;16;22;10;20;0.83;The dietician wants to select a menu to meet the nutritional guidelines;while minimizing the total cost per serving.;a.;Formulate a linear programming model for this problem.;b.;Solve the model by using the computer;c. If a serving of each of the;food items (other than milk) was limited to no more than a half pound, what;effect would this have on the solution?;22.;The Cabin Creek Coal (CCC) Company operates three mines in Kentucky and;West Virginia, and it supplies coal to four utility power plants along the East;Coast. The cost of shipping coal from;each mine to each plant, the capacity at each of the three mines and the demand;at each plant are shown in the following table;Plant;Mine;1;2;3;4;Mine Capacity;(tons);1;$ 7;$ 9;$10;$12;220;2;9;7;8;12;170;3;11;14;5;7;280;Demand (tons);110;160;90;180;The cost of mining and processing coal is $62 per ton at mine 1, $67;per ton at mine 2, and $75 per ton at mine 3. The percentage of ash and;sulfur content per;ton of coal at each mine is as follows;Mine;% Ash;% Sulfur;1;9;6;2;5;4;3;4;3;Each plant has different cleaning equipment. Plant 1 requires that the coal it receives;have no more than 6% ash and 5% sulfur, plant 2 coal can have no more than 5%;ash and sulfur combined, plant 3 can have no more than 5% ash and 7% sulfur;and plant 4 can have no more than 6% ash and sulfur combined. CCC wabts to determine the amount of coal;to produce at each mine and ship to its customers that will minimize its total;cost.;a.;Formulate a linear programming model for this problem.;b.;Solve this model by using the computer.;36.;Joe Henderson runs a small metal parts shop. The shop contains three;machines ? a drill press, a lathe, and a grinder. Joe;has three operators, each certified to work on all three machines. However, each operator performs better on;some machines than on others. The shop;has contracted to do a big job that requires all three machines. The times required by the various operators;to perform the required operations on each machine are summarized as;follows;Operator;Drill Press (min);Lathe (min);Grinder (min);1;23;18;35;2;41;30;28;3;25;36;18;Joe Henderson wants to assign one operator to each machine so that the topal;operating time for all three operators is minimized.;a.;Formulate a linear programming model for this problem.;b.;Solve the model by using the computer;c.;Joe?s brother, Fred, has asked him to hire his wife, Kelly, who is a;machine operator. Kelly can perform each;of the three required machine operations in 20 minutes. Should Joe hire his sister-in-law?;43.;The Cash and Carry Building Supply Company has received the following order;for boards in three lengths;Length;Order (quantity);7 ft.;700;9 ft.;1,200;10 ft.;300;The company has 25-foot standard-length boards in stock. Therefore, the standard-length boards must be;cut into the lengths necessary to meet order requirements. Naturally, the company wishes to minimize the;number of standard-length boards used.;a.;Formulate a linear programming model for this problem.;b.;Solve the model by using the computer;c.;When a board is cut in a specific pattern, the amount of board left over is;referred to as ?trim-loss.? Reformulate the linear programming model for this;problem, assuming that the objective is to minimize trim loss rather than to;minimize the total number of boards used, and solve the model. How does this affect the solution?Week 8 Assignment 1Assignment Week-8: Case Problem "Julia's Food Booth"Complete the "Julia's Food Booth" case problem on page 109 of the text.Note: Please address ONLY issues A, B, and C. You need not do part-DClick the link above to submit your assignment.Students, please view the "Submit a Clickable Rubric Assignment" in the Student Center.Instructors, training on how to grade is within the Instructor Center.Assignment 1. Linear Programming Case StudyYour instructor will assign a linear programming project for this assignment according to the following specifications.It;will be a problem with at least three (3) constraints and at least two;(2) decision variables. The problem will be bounded and feasible. It;will also have a single optimum solution (in other words, it won?t have;alternate optimal solutions). The problem will also include a component;that involves sensitivity analysis and the use of the shadow price.You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.Writeup.Your;writeup should introduce your solution to the project by describing the;problem. Correctly identify what type of problem this is. For example;you should note if the problem is a maximization or minimization;problem, as well as identify the resources that constrain the solution.;Identify each variable and explain the criteria involved in setting up;the model. This should be encapsulated in one (1) or two (2) succinct;paragraphs.After the introductory paragraph, write out the L.P.;model for the problem. Include the objective function and all;constraints, including any non-negativity constraints. Then, you should;present the optimal solution, based on your work in Excel. Explain what;the results mean.Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.Excel.As;previously noted, please set up your problem in Excel and find the;solution using Solver. Clearly label the cells in your spreadsheet. You;will turn in the entire spreadsheet, showing the setup of the model, and;the results.Clickhereto view the grading rubric for this assignment.Week 9 homeworkMAT540;Week;9 Homework;Chapter 5;6.;The Livewright Medical Supplies Company has a total of 12 salespeople it;wants to assign to three regions ? the South, the East, and the Midwest. A;salesperson in the South earns $600 in profit per month of the company, a;salesperson in the East earns $540, and a salesperson in the Midwest earns $375.;The southern region can have a maximum assignment of 5 salespeople. The company has a total of $750 per day;available for expenses for all 12 salespeople.;A salesperson in the South has average expenses of $80 per day, a;salesperson in the East has average expenses of $70 per day, and a salesperson;in the Midwest has average daily expenses of $50. The company wants to determine the number of;salespeople to assign to each region to maximize profit.;a.;Formulate an integer programming model for this problem;b.;Solve this model by using the computer.;10.;Solve the following mixed integer linear programming model by using the;computer;Maximize Z = 5 x1 + 6 x2 + 4;x3;Subject to;5 x1 + 3 x2 + 6 x3;? 20;x1 + 3 x2? 12;x1, x3? 0;x2;? 0 and integer;14.;The Texas Consolidated;Electronics Company is contemplating a;research and development program encompassing eight research projects. The company is constrained from embarking on;all projects by the number of available management scientists (40) and the;budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5;must also be selected (but not vice versa).;Following are the resource requirements and the estimated profit for;each project.;Project;Expense ($1,000s);Management Scientists required;Estimated;Profit;(1,000,000s);1;$ 60;7;$0.36;2;110;9;0.82;3;53;8;0.29;4;47;4;0.16;5;92;7;0.56;6;85;6;0.61;7;73;8;0.48;8;65;5;0.41;Formulate the;integer programming model for this problem and solve it using the computer.;20.;During the war with Iraq in;1991, the Terraco Motor Company produced a lightweight, all-terrain vehicle;code-named ?J99-Terra? for the military.;The company is now planning to sell the Terra to the public. It has five plants that manufacture the;vehicle and four regional distribution centers.;The company is unsure of public demand for the Terra, so it is considering;reducing its fixed operating costs by clos

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