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)
Nonnegativity: 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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(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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 Fall '08
 Srinivasan
 Linear Programming, Optimization, Dayton, Colt model

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