If, in a monopoly market, the demand function for a product is p = 180 - 0.80x and the revenue function is R = px, where x is the number of units sold and p is the price.
Suppose a company has fixed costs of $44,200 and variable cost per unit of 1/3x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of the product is 1948 - 2/3x dollars per unit.
(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x =
(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$
(c) Form the profit function P(x) from the cost and revenue functions.
P(x) =
Find maximum profit.
$
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$