Assignment
Problem Set 1
Thomas Ratzler is the manager of the Metropolitan Zoo which has a wide variety of animals. The animals' pattern of feeding is such that they must have at least 30 grams of protein and at least 20 grams of fat per feeding period. These nutrients are derived from two types of food. Type 1 food, which costs 18 cents per unit and supplies 2 grams of protein and 4 of fat; and Type 2 food, which costs 12 cents per unit and has 6 grams of protein and 2 of fat. Type 2food is bought under long-term contract requiring that at least 2 units of 2 to be used per serving. How much of each food must be bought to produce the minimum cost per serving? Show all the corner points in your solution.
Problem set 2
A community farm has 6000 square kilometers of land available to plant wheat and millet. Each kilometer square of wheat requires 9 gallons of fertilizer and insecticide and ¾ hour of labor to harvest. Each square kilometer of millet requires 3 gallons of fertilizer and insecticide and 1 hour of labor to harvest. The community has at most 40,500 gallons of fertility and insecticide and at most 5250 hours of labor for harvesting. If the profits per square kilometer are $60 for wheat and $40 for millet, how many square kilometers of each crop should the community plant in order to maximize profits? What is the maximum profit? Hint: x is the number of square kilometers of wheat and y is the number of square kilometers of millet.
Problem set 3
Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 250 hours of assembly time available, 180 hours of finishing time, and 20 hours of inspection time. To keep a balance, the number of chairs produced should be at least three times the number of tables. Also, the number of chairs cannot exceed 40 percent of the total production of tables and chairs. Formulate this as a linear programming problem. Carefully define all decision variables. Find the solution.
You can use QM to solve problem 3.