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.

Question

Myah Suarez

Mathematics

30 May, 08:57

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.

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Alaina Bautista · Answer 1

Selling price: x = 4

Maximum revenue: R (x) = 16

Step-by-step 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