Answer to Question #185725 in Economics for Loretta

Question

A manufacturer can produce radios at a cost of $10 a piece. It is also estimated that they are sold for x dollars, consumer will buy approximately 80-x radios each month.

Determine the expression for profit per radio

Express the manufacturers profit function as a function of price x

Determine the price at which the manufacturer’s profit will be greatest

Answer 1

Profit per radio equals to x-10 dollars.

Profit functon is (x-10)×(80-x)=80x-800-x^2+10x=90x-x^2-800.

To find the price at which the manufacturer's profit will be greatest we should find the maximum for function 90x-x^2-800. At this price the first derivative of function exuals to 0. So, (90x-x^2-800)'=0; 90-2x=0; x=45.