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Solution_ Homework2_Linear Programming

# Solution_ Homework2_Linear Programming - 311 Operations...

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311 Operations Management Fall 2008 Solution: Homework # 2 – Linear Programming 1. (30 points) Kristen decides to bake Deluxe Cookies (DC) in addition to her Standard Cookies (SC). She has enough dough on hand to make 30 cookies and enough chocolate chips to make 60 Standard cookies (SCCC). SC’s require 5 chocolate chips and sell for \$1.5 each while DC’s require 15 chocolate chips and sell for \$2 each. a. (15 points) Formulate a linear program to maximize revenue Decision Variables (can be X1, X2 or anything reasonable): SC: number of standard cookies (2pt) DC: number of deluxe cookies (2pt) Objective: maximize 1.5*SC + 2*DC (5pt) Constraints: Dough: SC+DC ≤ 30 (2pt) Chips: 5*SC+15*DC ≤ 5*60 = 300 (2pt) Non-negativity: SC, DC ≥ 0 (2pt) b. (12 points) Graph the feasible region for the linear program 3 points for each boundaries of the feasible region SC DC 30 20 60 (15,15) 30 1

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c. (3 points) For which product mix is revenue maximized? (15, 15) is the optimal (solving the binding constraints Dough: SC+DC=30 and Chips: 5*SC+15*DC=300) 2. (30 points) Question 8, page 69 in the book. a. (20 points) Formulate a linear program for this problem? Decision Variables (can be X1, X2 or anything reasonable):
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