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hw3 solution - BUAD 311 Homework 3 Linear Programming 1(30...

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1 of 2 (20, 10) D S 20 30 0 30 40 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 $3 × S+$4 × D s.t. S+D 30 5 × S+10 × D 200 S,D 0 b) (10 points) Graph the feasible region of this linear program. c) (5 points) 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.
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