Question

Find the number of units that produces a
maximum revenue given by R = 290x−0.2x
2, where R is the total revenue in dollars and x is the number of units sold.
Answer in units of units.

Answer 1

A quadratic equation have the standrad form:

a x ^ 2 + b x + c

R = 290 x − 0.2 x ^ 2 is quadratic equation:

R = − 0.2 x ^ 2 + 290 x + 0

The vertex of a quadratic parabola is the highest or lowest point, the maximum or minimum.

When a < 0 a quadratic parabola has a maximum.

In this equation : a = - 0.2 , b = 290 , c = 0


x coordinate of vertex:

x = - b / 2 a

In this case:

x = - 290 / [ 2 * ( - 0.2 ) ]

x = - 290 / - 0.4

x = 725

Replace this value in equation:

R = 290 x − 0.2 x ^ 2

Rmax = 290 * 725 - 0.2 * 725 ^ 2

Rmax = 210,250 - 0.2 * 525,625

Rmax = 210,250 - 105,125

Rmax = 105,125


725 units sold

Rmax = $105,125