Question

A candy store estimates that by charging x dollars each for a certain candy, it can sell 8−x candies each day. Use the quadratic function R(x)=− x 2 +8x to find the revenue received when the selling price of a candy is x . Find the selling price that will give the company the maximum revenue, and then find the amount of the maximum revenue.

Answer 1

Selling price: x = 4

Maximum revenue: R(x) = 16

Explanation:

The revenue received when the selling price of the candy is x is expressed with the equation R(x) = −x2 + 8x, which is a quadratic equation.

To find the value of x that gives us the maximum value of R(x), we need to find the value of x in the vertex of the quadratic equation. The formula to find this value of x is:

x_v = -b / 2a

where a and b are coefficients of the quadratic equation (in our case, a = -1 and b = 8).

So, we have that:

x_v = -8 / 2(-1) = -8 / -2 = 4

So the selling price of the candy that gives the maximum renevue is x = 4.

The maximum revenue will be:

R(4) = -4^2 + 8*4 = -16 + 32 = 16