Answer to Question #343196 in Calculus for chua

Question

The price-demand equation and the cost function for the production of HDTVs are

given, respectively, by

x = 7, 500 − 25p and C(x) = 120, 000 + 24x,

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 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, 500) and R′

(4, 200) and interpret these quantities.

(f) Graph the cost function and revenue function on the same coordinate system.

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′

(5, 500) and interpret these quantities.

Answer 1

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