Question

The revenue for a business, as a function of units produced, x, is shown below by R(x). C(×) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.

R(x) = 30x
C(x) = 6× + 1968

Answer 1

• P(x) = 24x -1968
• 82 units to break even

Explanation:

Given revenue function R(x) = 30x, and cost function C(x) = 6x +1968, you want the profit function and the value of x to break even.

Profit

Profit is the difference between revenue and cost:

P(x) = R(x) -C(x)

P(x) = 30x -(6x +1968)

P(x) = 24x -1968

Break even

The break even point is the number of units of production for zero profit.

P(x) = 0

24x -1968 = 0

x -82 = 0 . . . . . . . . divide by 24

x = 82 . . . . . . . . . add 82

82 units must be produced for the business to break even.