Question

BoxedNGone truck rentals calculates that its price function is p(x) = 200 − 2x, where p is the price (in dollars) at which exactly x trucks will be rented per day. Find the number of trucks that BoxedNGone should rent and the price it should charge to maximize revenue. Also find the maximum revenue.

Answer 1

Answer:

At Maximum point;

x(max) = 50

p(max) = $100

Maximum revenue = $5,000

Step-by-step explanation:

The price function is;

p(x) = 200 − 2x

where

p is the price (in dollars) at which exactly x trucks will be rented per day.

The revenue function R(x) can be written as;

R(x) = p(x) × x

Substituting p(x) equation;

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

To maximize R(x), at maximum point dR/dx = 0

differentiating equation 1;

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Substituting x = 50 into p(x)

p(50) = 200 - 2(50) = $100

p = $100

Maximum revenue is;

R = p × x = $100×50

R = $5,000