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For Incap T-shirts, the cost of producing x t-shirts can be expressed as C=0.6x2+0.52x+3200.

The revenue they gain can be expressed as R=100x. What is the maximum profit (revenue subtract cost) they can make? In other words, what is the maximum value of R−C? Express your answer to 2 significant figures.

Respuesta :

raphealnwobi

The maximum profit is $923.44 which is gotten when 83 T shirts are produced.

Given the function:

Profit = Revenue - Cost

Profit (P) = 100x - (0.6x²+0.52x+3200)

P = -0.6x² + 99.48x - 3200

The maximum profit is at dP/dx = 0, hence:

dP/dx = -1.2x + 99.48

0 = -1.2x + 99.48

1.2x = 99.48

x = 82.9

x ≅ 83

The maximum profit is at x = 83, hence:

P = -0.6(83)² + 99.48(83) - 3200

P = 923.44

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