Question;Module I;The Retread Tire Company recaps;tires. The fixed annual cost of the recapping operation is $ 60,000. The;variable cost of capping tires is $9. The company charges $25 to recap a tire.;a) For an annual volume of 120,000;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. thecompany's fixed monthly cost is $25, 000 and its;variable cost perpound of fertilizer is $0.15. Evergreen sells the fertilizer;for$0.40 per pound. Determine the monthly break-even volume for thecompany.;10. A large;research hospital has accumulated statistical data on its patients for an;extended period. Researchers have determined that patients who are smokers have;an 18% chance of contracting a serious illness such as heart disease, cancer;or emphysema, whereas there is only a.06 probability that a nonsmoker will;contract a serious illness. From hospital records, the researchers know that;23% of all hospital patients are smokers, while 77% are nonsmokers. For;planning purposes, the hospital physician staff would like to know the;probability that a given patient is a smoker if the patient has a serious;illness.;12. The Senate consists of 100 senators, of whom 34 are;Republicans and 66 are Democrats. A bill to increase defense appropriations is;before the Senate. Thirty-five percent ofthe Democrats and 70Va of the;Republicans favor the bill. The bill needs a simple majority to pass. Using a;probability tree, determine the probability that the bill will pass.;14 A metropolitan school system consists of;three districts?north, south, and central. The north district contains 25% of;all students, the south district contains 40%, and the central district;contains 35%. A minimum-competency test was given to all students, 10% of the;north district students failed, 15% of the south district students failed, and;5% of the central district students failed.;a. Develop a probability tree showing all;marginal, conditional, and joint probabilities.;b. Develop a joint probability table.;c. What is the probability that a student selected;at random failed the test?;Module 2;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 shown the profit or loss that could result from each investment.;Gasoline Availability;Investment Shortage Stable Supply Surplus;Motel $-8,000 $15,000 $20,000;Restuarant 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 (? =.4);e. Equal likelihood;Problem 2;The Steak and Chop Butcher Shop purchases steak from a local meatpacking;house. The meat is purchased on Monday at $2.00 per pound, and the shop sells;the steak for $3.00 per pound. Any steak left over at the end of the week is;sold to a local zoo for $.50 per pound. The possible demands for steak and the;probability of each are shown in the following table;Demand (lb.) Probability;20.10;21.20;22.30;23.30;24.10;1.00;The shop must decide how much steak to order in a week. Using Excel, construct;a payoff table for this decision situation and determine the amount of steak;that should be ordered, using expected value.;Module 3;The manager of the Carptet City;Outlet needs to make an accurate forecast of the demand for Soft Shag carpet;(its biggest seller). If the manager does not order enough carpet from the carpet;mill, customers will buy their carpet from one of Carpet City's many;competitors. The manager has collected the following demand data for the past 8;months;Month Demand;for Soft Shag Carpet (1,000 yd.);1 8;2 12;3 7;4 9;5 15;6 11;7 10;8 12;a. Compute a 3-month moving average forecast for;months 4 through 9.;b. Compute a weighted 3-month moving average;forecast for months 4 through 9. Assign weights of 0.55,0.33,and 0.12 to the;months in sequence, starting with the most recent month.;c. Compare the two forecasts by using MAD. Which;forecast appears to be more accurate?;Problem 38;Apperson and Fitz is a chain of clothing stores that cate$ lo high school and;college students.;It publishers;a quarterly catalog and ope?1es a Web site that feathers provocatively attired;males and females.;The Web site is very expensive to maintain, and company executives are not;sure whether the;number of hits at the site relate to sales (i.e. if people may be looking at the;site's pictures;only). The Web master has accumulated the following data for hits per month and;orders placed at;the Web site for the past 20 months;Develop a linear;regression model for these data and indicate whether there appears to be a;strong relationship between Web site hits and;orders. What would be the forecast for orders with 50,000 hits per months?;2, Interview someone in your crew who is in charge of providing food in;your submarine. Does;he/she use any model to insure an adequate amount of food for the crew and a;balanced diet? How is the cost of each diet;computed? Discuss how such a model can be used at your workplace.;Module 4;his is an;unformatted preview. Please download the attached document for the original;format.;Queuing Analysis;PROBLEM #8;The ticket booth on;the Tech campus is operated by one person, who is selling tickets for the;annual Tech versus;State football game;on Saturday. The ticket seller can serve an average of 12 customers per hour,on;average, 10;customers arrives;to purchase tickets each hour (poisson distributed). Determine the average time;a ticket buyer must wait;and the portion of;time the ticket seller is busy.;Arrival Rate;Service Rate;Average waiting;time in queue (Wq);Average waiting;time in the system (W);The portion of time;the ticket seller is busy;10;12;0.4167;0.5;83.33%;PROBLEM #10;The Dynaco;Manufacturing Company produces a particular product in an assembly line;operation. One of the machines;on the line is a;drill press that has a single assembly line feeding into it. A;partiallycompleted unit arries at the press to be worked;on every 7.5;minutes on average. The machine operator can process an average of 10 parts per;hour. Determine the average;number of parts;waiting to be worked on, the percentage of time the operator is working, and;the percentage of time the;machine is idle.;Arrival Rate;Service Rate;The average number;of parts waiting to be worked on;The pecentage of;time the operator is working;The percentage of;time the machine is idle;7.5;10;14.0625;75.00%;0.4;PROBLEM #12;The Peachtree;Airport in Atlanta serves light aircraft. It has a single runway and one air;traffice controller to land planes. It takes;an airplane 12;minutes to land and clear the runway. Planes arrive at the airport at the rate;of four per hour.;a. determine the;average number of planes that eill stack up, waiting to land;b. find the average;time a plane must wait in line before it can land.;c. Calculate the;average time it takes a plane to clear the runway once it has notified the;airport that it is in the vicinity and wants to land.;d. The FAA has a;rule than an air traffic controller can, on average, land planes a maximum of;45 minutes out of every hour. There;must be 15 idle;time available to releive the tension. Will this airport have to hire an extra;air traffic controller?;Problem #14;During registration;at State University every semester, students in the college of business must;have their courses approved;by the college;advisor. It takes the advisor an average of 2 minutes to approve each schedule;and students arrive at the advisor's;office at the rate;of 28 per hour.;a. compute L;Lq,W,Wq, and U.;b. the dean of the;college has received a number of complaints from students about the length of;time they must wait to have their schedules;approved. The dean;feels that waiting 10.00 minutes to get a schedule approved is not;unreasonable. Each assistant the dean assigns to;the adviser's;office will reduce the average time required to approve a schedule by 0.25;minute, down to a minimum time of 1.00 minute to;approve a schedule.;How many assistants should the dean assign to the advisor?;Inventory Management;Problem # 2;Hayes electronics;assumed with certainty that the ordering cost is $450 per order and the;inventory;carrying cost is;$170 per unit per year. However, the inventory model parameters are frequently;only;estimates that are;subject to some degree of uncertainty. Consider four cases of variation in the;model;parameters as;follows: (a) both ordering cost and carrying cost are 10% less that originally;estimated;(b) both ordering;cost and carrying cost are 10% higher than originally estimated, (c) ordering;cost is;10% higher and;carrying cost is 10% lower than originally estimated, and (d) ordering cost is;10%;lower and carrying;cost is 10% higher than originally estimated. Determine the optimal order;quantity;and total inventory;cost for each of the four cases. Prepare a table with values from all four;cases and;compare the;sensitivity of the model solution to changes in parameter values.;Problem #4;The Western Jeans;Company purchases denim from Cumberland Textile Mills. The Western Jeans;Company uses;235,000 yards of denim per year to make jeans. The cost of ordering denim from;the;textile company is;$250 per order. It costs Western $1.65 per yard annually to hold a yard of;denim in;inventory.;Determine the optimal number of yards of denim the Western Jeans Company should;order, the minimum;total annual inventory cost, the optimal number of orders per year, and the;optimal time;between orders.;Module 5;6.;Given the;following network with activity times in months, determine the earliest and;latest activity times and slack for each activity.Indicate the critical path;and the project duration.;(see;diagram in the attached file);13. Consider;the network in problem 6, but with the following new time estimates for each;activity;time estimates (mo);Activity a m b;1 4 8 12;2 6 10 15;3 2 10 14;4 1 4 13;5 3 6 9;6 3 6 18;7 2 8 12;8 9 15 22;9 5 12 21;10 7 20 25;11 5 6 12;12 3 8 20;Determine the following;a. Expected activity times;b. Earliest activity times;c. Latest activity times;d. Activity slack;e. Critical path;f. Expected project duration and variance;17. For the CPM/PERT network in Problem 13, determine the probability;that the network duration;will exceed 50 months.;4. Good project managers;are highly sought in business and industry. Describe your experience, if you have worked as a project manager.;Alternatively, you can interview someone;who may have led a large project in the past.;Module 6;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;products 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.;Please see the attachment.;The;Pinewood Furniture Company produces chairs and tables from two resources-labor;and wood. The company has 80 hours of labor and 36 pounds of wood available;each day. Demand for chairs is limited to 6 per day. Each chair requires 8;hours of labor and 2 pounds of wood, whereas a table requires 10 hours of labor;and 6 pounds 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 table to;produce each day in order to maximize profit.;a. Formulate a linear programming model for this problem.;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 1 gram of ingredient 2 contributes 1 unit;of antibiotic 1, the drug requires 6 units. 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 in order to meet the antibiotic requirements at the;minimum cost.;a. Formulate a linear programming model for this 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. Each type of;biscuit requires 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.;On a separate spreadsheet, Solve the linear programming;model formulated above graphically.;a);How much extra sausage and ham are left over at;the optimal solution point? Is there any;idle labor time?;b);What would the solution be if the profit for a;ham biscuit were increased from $0.50 to $0.60?;c);What would be the effect on the optimal solution;if the manager could obtain 2 more pounds of flour?;24. 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 Sausage Ham Flour;Sausage (X1) 0.010 0.10 0.00 0.04;Ham (X2) 0.024 0.00 0.15 0.04;1. I dentify and explain ther shadow prices for each resource constraints.;2. Which resource constaints profit the most;3. Identify the sensitivity ranges for the profit of a sausauge biscuit and the;amount of saisage available. Explain these sensitivity ranges;Module 7;12. Betty Mallow, owner of the Eagle Tavern in Pittsburgh, is preparing for;Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks;three brands of beer- yodel, shotz, and rainwater. The cost per gallon (to the;tavern owner) of each brand is as follows;Brand Cost/Gallon;Yodel $1.50;Shotz $0.90;Rainwater $0.50;The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells;Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater;at $1.75 per gallon. Based on past football games, Betty has determined the;maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and;300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of;beer, Betty wants to stock up completely. Betty wants to determine the number;of gallons of each brand of beer to order so as to maximize profit.;A. Formulate a linear programming model for this problem.;B. Solve the model by using the computer.;problem;Brooks City has three consolidated high;schools, each with a capacity of 1,300 students. The school board has partitioned;the city into five busing districts - north, south, east, west, and central -;each with different high school student populations. the three schools are;located in the central, west, and south districts. Some students must be bused;outside of theri district, and the school board wants to minimize the total bus;distance traveled by these students. The average distances from each district;to the three schools and the total student population in each district are as;follows.;Distance;(Miles);District Central School West School South School Student Population;District Distance (miles) Student Central West South Population School;School School North 8 11 14 700 South 12 9 - 300 East 9 16 10 900 West 8 - 9;600 Central - 8 12 500 The school board wants to determine the number of;student to bus from each district to each school to minimize the total busing;miles traveled.;a);formulate a linear programming model for this problem;b);solve the model by using the computer PLEASE use excel solver. Joe Henderson runs a small metal part;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 other. 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 22 18 35;2 41 30 28;3 25 36 18;16.;The athletic boosters club for Beaconville has planned a 2-day fund-raising drive;to purchase uniforms for al the local high schools and to improve facilities.;Donations will be solicited during the day and night by telephone and personal;contact. The boosters club has arranged for local college students to donate;their time to solicit donations. The average donation from each type of contact;and the time for a volunteer to solicit each type of donations are as follows;Average donation ($) Average Interview Time (min.);Phone;Personal Phone Personal;Day 16 33 6 13;Night 17 37 7 19;The boosters club has gotten several businesses and car dealers to donate;gasoline and cars for the college students to use to make a maximum of 575;personal contacts daily during the fund-raising drive. The college students;will donate a total of 22 hours during the day and 43 hours at night during the;drive.;The president of the booster club wants to know how many different types of;donor contacts to schedule during the drive to maximize the total donations.;Formulate and solve an integer program between the integer and non-integer;rounded-down solutions to this problem?;24 Harry and Melissa Jacobson;produce handcrafted furniture in a workshop on their farm. They have obtained a;load of 600 board feet of birch from a neighbor and are planning to produce;round kitchen tables and ladder-back chairs during the next 3 months. Each;table will require 30 hours of labor, each chair will require 18 hours, and;between them they have a total of 480 hours of labor available. A table;requires 40 board feet of wood to make, and a chair requires 15 board feet. A;table earns the couple $575 in profit and chair earns $120 in profit. Most;people who buy a table also want four chairs to go with it, so for every table;that is produced, at least four chairs must also be made, although additional;chairs can also be sold separately. Formulate and solve an integer programming;model to determine the number of tables and chairs the Jacobsons should make to;maximize profit.
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