Answer to Question #328376 in Microeconomics for fred

Question

A manufacturer can produce radios at a cost of $10 apiece an estimated that if they are sold for x dollars, consumers will buy approximately80-x radios each month. Express the manufacturer’s monthly profit as a function of the price x, graph this function, and determine the price at which the manufacture’s profit will be greatest.

Answer 1

Profit = (number of radios sold)$\cdot$(profit per radio)

Number of radios sold = 80 – x

Let P(x) denotes the profit and conclude that

$P(x) = (80 -x)(x -10) = -x^2 + 90x -800$