Suppose x represents the quantity of items produced and sold.
The price-demand function p(x) calculates the price per item.
The revenue function R(x) calculates the total money collected by selling x items at a price p(x), R(x) = x p(x).
The cost function C(x) calculates the cost to produce x items. The value C(0) is called the fixed cost or start-up cost.
The average cost function C(x) = C(x) calculates the cost per item when making x items. x
Here, we necessarily assume x > 0.
The profit function P(x) calculates the money earned after costs are paid when x items are produced and sold, P (x) = (R â C)(x) = R(x) â C(x).
10. (See textbook page 82 for definitions of the economic functions used in this problem.) Company XYZ manufactures and sells widgets. The cost, in dollars, to produce x widgets is given by CCx) 2137.50 7.50x for x20, and the price-demand function, in dollars per widget, is pCx- 24 -0.015x for 0 Sx 1600 (a Find and interpret CO2500. (b) Find and interpret CO250). (Note that CC) is the average cost function.) (c) Find and simplify the expression for the revenue function RO). (d Find and simplify the expression for the profit function PC). Note that pC) and Poc are different functions (e) Find and interpret PO250), where PC is the profit function in part (d)
