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Unformatted text preview: BUAD 311 Homework 3: Linear Programming 1. (30 points) Kristen decided to bake Deluxe Chocolate Chip Cookies (DCCCs), in addition to her Standard Chocolate Chip Cookies (SCCCs). She has enough dough on-hand to make 30 cookies and enough chocolate chips to make 40 SCCCs. SCCCs require 5 chocolate chips each and sell for $3 each while DCCCs require 10 chocolate chips each and sell for $4 each. a) (15 points) Formulate this problem as a linear program that maximizes revenue. S = number of standard cookies to make D = number of deluxe cookies to make LP: max $3S+$4D s.t. S+D 30 5S+10D 200 S,D 0 b) (10 points) Graph the feasible region of this linear program. D 30 20 (20, 10) 0 c) (5 points) 30 40 S For what product mix of SCCC and DCCC cookies is revenue maximized? Is this product mix unique or are there other solutions that result in the same revenue? Solution: The unique optimal solution is S*=20 and D*=10 with objective function value of $100. 2. (10 points) Kristen thinks that wrapping the cookies in tissue paper will make them seem more upscale and thus increase her profit. It takes one sheet of tissue paper to wrap each cookie. The tissue paper costs $.50 per sheet. Wrapped SCCC cookies retail for $3.50 each while wrapped DCCC cookies retail for $6.75 each. Will this change the optimal mix found in 1(c)? Please explain your results. Answer: The feasible region remains the same (as in Problem 1). The new information changes only the objective function value to $122.50 but not the constraints.
1 of 2 3. (30 points) Problem 4 on page 68 in the textbook. a) (20 points) Formulate this problem as a linear program. A = amount of food A in lbs. B = amount of food B in lbs. LP: min $0.75A+$0.15B s.t. A 2 600A+900B 1800 600A+900B 3600 200A+700B 1400 400A+100B 400 A,B 0 b) (10 points) Solve this linear program using the Excel Solver. Solution: A*=0.53846, B*=1.84615, objective function value = $0.68077 4. (30 points) Problem 8 on page 69 in the textbook. a) (20 points) Formulate this problem as a linear program. E = barrels of Expansion Draft to produce B = barrels of Burning River to produce LP: max $20E+$8B s.t. 8E+2B 500 4E+3B 400 6B 300 E,B 0 b) (5 points) Solve this linear program using the Excel Solver. Solution: E*=50 and B*=50 with objective function value of $1,400 c) (5 points) What is the shadow price of hops? What does the shadow price of hops mean in this case? Answer: $0 (extra hops worth nothing to the brewery) 2 of 2 ...
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This note was uploaded on 05/11/2008 for the course BUAD 311 taught by Professor Vaitsos during the Spring '07 term at USC.
- Spring '07