Publishing—Price/Demand: The Between the Lines Publishing Company determines that the price-demand function for a new book is , with fixed costs of $12,000 and variable costs of 4.5 dollars per book.
(a) Determine the cost function C and the revenue function R.
(b) Find the profit function P.
(c) Find the smallest and largest production levels x so that the company realizes a profit. (That is, find the smallest and largest independent values so that the revenue is greater than the cost.)
(d) Compute the marginal profit function P′(x).
(e) Evaluate P′(2500) and interpret the result.
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