Question

The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x) = 0.23x. The profit (in millions of dollars) from the sale of x units is given by P(x) = 0.083x - 1.1 a) Find the cost equation. (b) What is the cost of producing 9 units? (c) What is the break-even point?

Answer 1

R(x) = 0.23x

p(x) = 0.083x - 1.1

A) Cost Equation: R(x) - P(x)

0.23x - (0.083x - 1.1)

0.23x - 0.083x + 1.1

0.147x + 1.1

B) What is the cost of producing 9 units? x = 9

Using: 0.147x + 1.1

0.147 x 9 - 1.1

1.323- 1.1 = $0.223

(C) Break-even point means: when cost equation. = R(x)

0.147x + 1.1 = 0.23x

0.23x -0.147x = 1.1

0.083x = 1.1

x = 1.1/0.083

x = 13.25

So, the break-even point will be by using any of the cost or Revenue equation: 0.23x = 0.23(13.25) = 3.0475