865 words - 4 pages

Assignment I (Due on Sept. 22 2015)

1. Consider the following LP problem.

MAX: 3x1+2x2

Subject to: 3x1+2x2≤300

6x1+3x2≤480

3x1+6x2≤480

x1,x2≥0

a. Sketch the feasible region for this model.

b. What is the optimal solution?

c. Identify any redundant constraints in this model.

2. Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour cutting, 30 minutes in ...view middle of the document...

a. Formulate an LP model for this problem.

b. Sketch the feasible region for this problem.

c. What is the optimal solution?

4. Tuckered Qutfitters plans to market a custom brand of packaged trail mix. The ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts, and Almonds costing, respectively, $2.50, $1.50, $2.00, $3.50 and $3.00 per pound. The vitamin, mineral and protein content of each of the ingredients (in grams per pound) is summarized in the following table along with the calories per pound of ingredient:

| Raisins | Grains | Chocolate | Peanuts | Almonds |

Vitamins | 20 | 10 | 10 | 30 | 20 |

Minerals | 7 | 4 | 5 | 9 | 3 |

Protein | 4 | 2 | 1 | 10 | 1 |

Calories | 450 | 160 | 500 | 300 | 500 |

The company would like to identify the least costly mix of these ingredients that provides at least 40 grams of vitamins, 15 grams of minerals, 10 grams of protein, and 600 calories per 2-pound package. Additionally, they want each ingredient to account for at least 5% and no more than 50% of the weight of the package.

a. Formulate an LP model for this problem.

b. Implement your model in a spreadsheet and solve it.

c. What is the optimal mix, and how much is the total ingredient cost per package.

5. Incline Electronics produces three different products in a plant that is open 40 hours per week. Each product requires the following processing times (in hours) on each of three machines.

| Product 1 | Product 2 | Product 3 |

Machine 1 | 2 | 2 | 1 |...

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