If C (x) = 19000 + 600x - 2.6x2 + 0.004x3 is the cost function and p (x) = 1800 - 8x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

Question

Dania Schwartz

Mathematics

19 July, 11:24

If C (x) = 19000 + 600x - 2.6x2 + 0.004x3 is the cost function and p (x) = 1800 - 8x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

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Ireland Moran · Answer 1

Marginal revenue will be given by:

R (x) = C (x) - P (x)

C (x) = 19000 + 600x - 2.6x2 + 0.004x3

P (x) = 1800 - 8x

Thus:

R (x) = 19000 + 600x - 2.6x2 + 0.004x3 - (1800 - 8x)

R (x) = 17200+592x-2.6x2+0.004x3