Question;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 closing one or more plants, even though;it would incur an increase in transportation costs. The relevant costs for the problem are;provided in the following table. The;transportation costs are per thousand vehicles shipped, for example, the cost of shipping 1,000 vehicles;from plant 1 to warehouse C is $32,000.;From Plant;Transportation Costs ($1000s);to Warehouse;Annual Production Capacity;Annual Fixed Operating Costs;A;B;C;D;1;$56;$21;$32;$65;12,000;$2,100,000;2;18;46;7;35;18,000;850,000;3;12;71;41;52;14,000;1,800,000;4;30;24;61;28;10,000;1,100,000;5;45;50;26;31;16,000;900,000;Annual;Demand;6,000;14,000;8,000;10,000;Formulate and solve an integer;programming model for this problem to assist the company in determining which;plants should remain open and which should be closed and the number of vehicles;that should be shipped from each plan to each warehouse to minimize total cost.Week 10 Homework SubmissionClick the link above to submit your homework assignment.Complete the following problems from Chapter 6:Problems 4, 6, 36, 48Week 8 discussionPractice;setting up linear programming models for business applications;Select an even-numbered LP problem;from the text, excluding 14, 20, 22, 36 (which are part of your homework;assignment). Formulate a linear programming model for the problem you select.Week 9 discussionWeek 9 Discussion;Discuss;characteristics of integer programming problems;Select one (1) of the following;topics for your primary discussion posting;?;Explain how the applications of;Integer programming differ from those of linear programming. Give specific;instances in which you would use an integer programming model rather than an LP;model. Provide real-world examples.;?;Identify any challenges you have in;setting up an integer programming problem in Excel, and solving it with Solver.;Explain exactly what the challenges are and why they are challenging. Identify;resources that can help you with that.;Week 10 discussionWeek 10 Discussion;Discussion assignment and;transshipment problems;Select one (1) of the following;topics for your primary discussion posting;?;Explain the assignment model and how;it facilitates in solving transportation problems. Determine the benefits to be;gained from using this model.;?;Identify any challenges you have in;setting up an transshipment model in Excel, and solving it with Solver. Explain;exactly what the challenges are and why they are challenging. Identify;resources that can help you with that.
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