Cost analysis. Letbe the price–demand equation and cost function, respectively, for the ma...

Cost analysis. Let

be the price–demand equation and cost function, respectively, for the manufacture of umbrellas.

(A) Find the marginal cost, average cost, and marginal average cost functions.

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(B) Express the revenue in terms of x, and find the marginal revenue, average revenue, and marginal average revenue functions.

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(C) Find the profit, marginal profit, average profit, and marginal average profit functions.

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(D) Find the break-even point(s).

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(E) Evaluate the marginal profit at x = 1,000, 1,150, and 1,400, and interpret the results.

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(F) Graph R = R(x) and C = C(x) on the same coordinate system, and locate regions of profit and loss.