311 Operations Management
Spring 2009
Homework 2: Linear Programming
1.
(30 points)
For the following LP,
maximize
x
1
+ 2
x
2
subject to
x
1
+
x
2
24
10
x
1
+ 20
x
2
300
x
1
≥
0
x
2
≥
0
(a)
(10 points) Graph the feasible region for the linear program. Clearly label all the
intercepts.
(b)
(8 points)
Find the solution of the LP. Is it unique?
(c)
(12 points) Supposed the objective function is changed to
2
1
3
2
x
x
, do you need to
regraph the feasible region of this LP? Why? What is the solution for the new LP? Is it
unique?
2.
(35 points)
Ctown brewery brews two beers: Expansion Draft and Burning River.
Expansion draft sells for $20 per barrel while Burning River sells for $8 per barrel.
Producing a barrel of Expansion Draft takes 8 pounds of corn and 4 pounds of hops.
Producing a barrel of Burning River requires 2 pounds of corn, 6 pounds of rice and 3
pounds of hops. The brewery has 500 pounds of corn, 120 pounds of rice, and 270
pounds of hops. Ctown would like to determine the optimal mix in order to maximize
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 Fall '07
 Vaitsos
 Management, Operations Research, Linear Programming, Optimization, Burning River

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