Manufacturing—Price/Demand: The Deluxe Furniture Company determines that the price–demand...

Manufacturing—Price/Demand: The Deluxe Furniture Company determines that the price–demand function for its new bookshelf is

The fixed costs are $10,000 and variable costs are 150 dollars per unit. Redo parts (a) through (e) in Exercise 1.

Exercise 1

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.

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(b) Find the profit function P.

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(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.)

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(d) Compute the marginal profit function P′(x).

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(e) Evaluate P′(2500) and interpret the result.