HW 3 Solutions

# HW 3 Solutions - Objective minimize 6 R 10 D Constraints...

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Fried Chicken Problem Solution STOR 112 You are planning a big party to watch the UNC vs. Duke game, and you want to pick up some delicious fried chicken. You go to Carolina Fried Chicken (CFC), and they tell you there are two types of chicken buckets: Regular buckets, which have 12 wings and 3 drumsticks, and Deluxe buckets, which have 12 wings and 8 drumsticks. Regular buckets are \$6 and Deluxe buckets are \$10. Your know you will need to have at least 180 pieces of chicken to keep your friends from being hungry. Your roommate loves drumsticks, and she insists that the number of drum- sticks shouldn’t be less than half the number of wings. How many of each type of bucket should you buy to spend the least amount of money? 1. Write down the variables, objective function and constraints. Variables: R = number of regular buckets and D = number of deluxe buckets.

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Unformatted text preview: Objective: minimize 6 R + 10 D Constraints: • 15 R + 20 D ≥ 180 • Number of drumsticks ≥ 1/2*(number of wings), which is written as 3 R + 8 D ≥ 1 2 (12 R + 12 D ), which reduces to 3 R ≤ 2 D or 3 R-2 D ≤ 0. 2. Graph the feasible region. 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 R (Regular) D (Deluxe) 3 R ≤ 2 D , or 3 R-2 D ≤ Corner Point (4 , 6) 15 R + 20 D ≥ 180 Corner Point (0 , 9) 3. Identify the extreme points. The corner points are R = 0, D = 9; and R = 4, D = 6. 4. Find the objective value at each corner point. At (0 , 9), the objective value is 90. At (4 , 6), the objective value is 84. Since the objective is min, we choose (4 , 6) as the optimal. 5. Solve the problem in Excel. 6. Interpret your solution. We should buy 4 regular buckets and 6 deluxe buckets at a cost of \$84. 2...
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HW 3 Solutions - Objective minimize 6 R 10 D Constraints...

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