Homework2_Linear Programming_Solution

Homework2_Linear Programming_Solution - 311 Operations...

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311 Operations Management Spring 2009 Homework 2 Solution: Linear Programming 1. (30 points) For the following LP, maximize x 1 + 2 2 subject to 1 + 2 24 10 1 + 20 2 300 § 0 (a) (10 points) Graph the feasible region for the linear program. Clearly label all the intercepts. 1 point each for labeling points in red; 2 points for finding the correct intersection point (18,6); 3 points for correctly identify the feasible region. (b) (8 points) Find the solution of the LP. Is it unique? Any point on the line between (18,6) and (0,15). No. it is not unique. 5 points for finding a point as the solution; 3 points for knowing that it is now unique (b) (12 points) Supposed the objective function is changed to 2 1 3 2 x x + , do you need to re-graph the feasible region of this LP? Why? What is the solution for the new LP? Is it unique? No. Because the constraints remain unchanged. The new solution is (18,6). It is unique. 3 points for each question. (18,6) 0 24 30 15 24 2 x
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2. (35 points) C-town 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. C-town would like to determine the optimal mix in order to maximize the revenue. (a)
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Homework2_Linear Programming_Solution - 311 Operations...

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