Homework_3_LinearProgram_Solution

# Homework_3_LinearProgram_Solution - 311 Operations...

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311 Operations Management Fall 2007 Homework 3: Linear Programming Due 9/25/2007 Solutions 1. (30 pts.) You are making standard and deluxe chocolate chip cookies. You have enough dough on hand to make 2 dozen cookies. You have enough chocolate chips on hand to make 30 standard cookies. Standard cookies have 10 chocolate chips each and deluxe cookies have 20 chocolate chips each. Standard cookies retail for \$1 each and deluxe cookies retail for \$3 each. (a) (15 pts.) Formulate a linear program to maximize revenue. Decision variables: x 1 : number of standard cookies (2pt) x 2 : number of deluxe cookies (2pt) Objective: maximize x 1 + 3 x 2 (5pts) Constraints: x 1 + x 2 24 (2pts) 10 x 1 + 20 x 2 300 (2pts) x 1 ,x 2 0 (2pts) (b) (10 pts.) Graph the feasible region for the linear program. (18, 6) x 2 x 1 15 24 0 24 30 1

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(c) (5 pts.) For which product mix of standard and deluxe is revenue max- imized? What is the maximum revenue? Is your choice unique? Revenue is maximized when 15 deluxe cookies are made. The maxi- mum revenue is \$45. The choice is unique. (5pts) 2. (10 pts.)
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