Determine the cost in dollars of producing x units of the game console for a retailer: C(x) = 80x + 150.

Question

1. Find an expression for the average cost function C̅(x).
2. Solve and interpret C̅(x) < 100

Answer 1

Average cost function C̅(x)=C(x)/x or more simply the total cost divided by the number of units produced. Hence, C̅(x)=(80x+150)/x or C̅(x)= 80 + 150/x .

If C̅(x)<100, it means that the average cost per unit is less than 100.

Plugging in for what C̅(x) is we get the following inequality:

80+150/x<100

150/x<20

150<20x

150/20<x

7.5<x

The average cost per unit is less than $100 only when you are producing 8 or more units.