3. (3 points) TruckCo manufactures two types of trucks: 1 and 2. Each truck must

Question

3. (3 points) TruckCo manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled, if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contribute $500. Formulate an LP that will maximize Trucko's profit.

Explanation / Answer

Let x, y number of trucks of type 1 and 2 to be produced respectively.
Maximize (Total Profit) Z=300 x +500 y
Subject to the constraints
(a) Painting Shop
800 x +700 y leq 24
(b) Assembly Shop
1500 x +1200 yleq 24
and x, y geq 0

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