Mat 540 Week 8 Homework Essay

1333 words - 6 pages

MAT 540 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 ...view middle of the document...

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...

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