311 Operations Management
Spring 2008
Homework 3: Linear Programming
Due 2: February 11, 2008
1. (30 points)
Kristen decides to bake Deluxe Chocolate Chip Cookies (DCCC) in
addition to her Standard Chocolate Chip Cookies (SCCC).
She has enough dough on
hand to make 30 cookies and enough chocolate chips to make 40 Standard cookies
(SCCC).
SCCC’s require 5 chocolate chips and sell for $3 each while DCCC’s require
10 chocolate chips and sell for $4 each.
(a)
(15 points)
Formulate a linear program to maximize revenue.
Decision Variables (These could also be X1, X2 or anything reasonable as long as it is
consistent):
SCCC: number of standard cookies (2pt)
DCCC: number of deluxe cookies (2pt)
Objective: maximize 3*SCCC + 4*DCCC (5pt)
Constraints:
Dough: SCCC+DCCC
≤
30 (2pt)
Chips:
5*SCCC+10*DCCC
≤
200 (2pt)
Nonnegativity: SCCC,DCCC
≥
0 (2pt)
(b)
(10 points)
Graph the feasible region for the linear program.
(c)
(5 points)
For which product mix of SCCC and DCCC is revenue maximized?
Is the
choice unique or are there other solutions which provide the same revenue?
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 Spring '07
 Vaitsos
 Management, Optimization, linear program, chocolate chip cookies, SCCC

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