XYZ Tire Manufacturing makes two types of tires, Brand A and Brand B. The profit

Question

XYZ Tire Manufacturing makes two types of tires, Brand A and Brand B. The profit on the sale of the Brand A tire is $31 and the profit on the Brand B tire is $28. The time it takes to produce the Brand A tire is 21 minutes and the time it takes to produce Brand B tire is 10 minutes. There are a total of 13230 work minutes available during the week. Due to plant restrictions, the plant cannot produce more than 540 Brand A tires during the week and no more than 378 Brand B tires during the week. If the company produces tires at a level that maximized the profit, what is that maximum profit?

Explanation / Answer

Below is the LPP formulation,

maximize Z = 31x + 28y subject to
21x + 10y <= 13230
x <= 540
y <= 378

Solving this graphically gives below solution

Vertex Lines Through Vertex Value of Objective
(540,189) 21x+10y = 13230; x = 540 22032
(450,378) 21x+10y = 13230; y = 378 24534 Maximum
(540,0) x = 540; y = 0 16740
(0,378) y = 378; x = 0 10584
(0,0) x = 0; y = 0 0

Maximum profit = $24534

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