Concept explainers
Revenue, cost, and profit. The price–demand equation and the cost function for the production of HDTVs are given, respectively, by
where x is the number of HDTVs that can be sold at a price of $p per TV and C(x) is the total cost (in dollars) of producing x TVs.
- (A) Express the price p as a function of the demand x, and find the domain of this function.
- (B) Find the marginal cost.
- (C) Find the revenue function and state its domain.
- (D) Find the marginal revenue.
- (E) Find R′(3,000) and R′(6,000) and interpret these quantities.
- (F) Graph the cost function and the revenue function on the same
coordinate system for 0 ≤ x ≤ 9,000. Find the break-even points and indicate regions of loss and profit - (G) Find the profit function in terms of x.
- (H) Find the marginal profit.
- (I) Find P′(1,500) and P′(4,500) and interpret these quantities.
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