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A manufacturer finds it costs him x + 5x + 7 dollars to produce x tons of an item. At 2 production levels above 3 tons, he must hire additional workers, and his costs increase by 3(x - 3) dollars on his total production. If the price he receives is $13 per ton regardless of how much he manufactures and if he has a plant capacity of 10 tons, what level of output maximizes his profits?

Respuesta :

Answer: The maximum = 3 tons

Step-by-step explanation:

The cost function C(x) = x + 5x + 7

P(×) = 13x - x^2 - 5x -7

If x <3

P= x^2 +8x -7

Differentiating to get x

dp/dx = -2x + 8

X= 8/2

C=4

Maximum will be 3 tons

When x=3

P= 13x - x^2 -5x +7 -3x + 9

When x>3

dp/dx = x^2+5x +2

X = 5/2 = 2.5

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