Question

A toy store owner estimates that by charging x dollars each for a certain toy, he can sell 40−x toys each week. The quadratic equation R=−x^2+40x is used to find the revenue, R , received when the selling price of a toy is x . Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.

Answer 1

Answer:x=20

Step-by-step explanation:

Given

selling Price of Toy is x dollars

he can sell 40-x toys each week

Thus Revenue Generated from selling 40-x toys at x dollar can be given by

$R=-x^2+40x$

To get maximum Revenue differentiate R with respect to x  and equate it to 0

therefore $\frac{\mathrm{d} R}{\mathrm{d} x}=-2x+40$

$-2x+40=0$

$x=20$

thus for maximum Revenue owner sells 20 toys each week

Max Revenue $R=-(20)^2+40\times 20=-400+800= 400$