Question

A manufacturer can produce at a cost of $10 apiece an estimated if they are sold for x dollars, consumers will buy approximately 80-x radios each month. Express the manufacturer's profit as a function of the price x, graph this function and determine the price at which the manufacturers profit will be greatest.

Answer 1

Begin by stating the desired relationship in words:

Profit = (number of radios sold) (profit per radio)

Now replace the words by algebraic expressions. You know that :

Number of radios sold = 80 – x

and since the radios are produced at a cost of $10 apiece and sold for x dollars apiece,

It follows that profit per radio = 80 − x

Let P(x) denotes the profit and conclude that

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