Question

Suppose a baby food company has determined that its total revenue R for its food is given by R = − x 3 + 33 x 2 + 720 x where R is measured in dollars and x is the number of units (in thousands) produced. What production level will yield a maximum revenue?

Answer 1

A production level of 30 thousand units (x = 30)

Explanation:

To find the production level (value of x) that will yield the maximum revenue, we can take the derivative of the function R in relation to x and find when it is equal to 0:

dR/dx = -3x2 + 66x + 720 = 0

x2 - 22x - 240 = 0

Solving the quadratic equation using Bhaskara's formula, we have:

Delta = (-22)^2 + 4*240 = 1444

sqrt(Delta) = 38

x1 = (22 + 38)/2 = 30

x2 = (22 - 38)/2 = -8

The negative value is not valid for our problem, so we have that the value that gives the maximum revenue is x = 30