Answers must be completed in the Excel spreadsheet attached. MAT540 Week 8 Homework Chapter 4 1. 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. 2. As a result of a recently passed bill, a congressmans 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 staffs 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. 3. 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.) Carbohydrates (g/lb.) Fat (g/lb.) Cholesterol (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? 4. 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 ea…
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