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1. Solve the following linear programming problem graphically using the corner-point method.
Maximize profit = 4X + 6Y
Subject to: X + 2Y ≤ 8
5X + 4Y ≤ 20
X, Y ≥ 0
What are the X and Y values that maximize the profit? For full credit, please list all the corner points in this case and compute the corresponding objective values of each of the corner points.
2. The Electrocomp Corporation manufactures two electrical products: air conditioner and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time is available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for $15 profit.
Let X denote the number of air conditioners to be manufactured and Y denote the number of fans to be assembled. Formulate the linear programming production-mix situation. A model similar to the one on Slide 17 of the lecture slides of Week 14 is expected.
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