In each problem below, the average cost function by dividing the cost function by the variable representing the quantity. For a cost function *C*(*Q*), the average cost function is

The marginal average cost function is the derivative of the average cost function.

**Problem 1** Suppose the total cost function for a product is

where *Q* is the number of units produced.

- Find the average cost of producing 20 units.
- Find the average cost function.
- Find the marginal average cost function.
- Find and interpret the marginal average cost when 20 units are produced.

This means that each of the 20 units costs an average of .1386 hundred dollars or $13.86.

In this board they have used the fact that dividing by *Q* is the same as multiplying by 1/*Q*.

Although it is OK to leave the derivative unsimplified, they need to put in 20. So it is best to do some algebra before putting in the value. Since -0.006 is the slope of the tangent line on the average cost function, the units on it is hundreds of dollars per unit per unit:

This means that if production is increased by 1 unit, the average cost will drop by 0.006 hundred dollars per unit.

**Problem 2** Suppose the total cost function for a product is

where *x* is the number of units produced.

- Find the average cost of producing 10 units.
- Find the average cost function.
- Find the marginal average cost function.
- Find and interpret the marginal average cost when 10 units are produced.

This value tells us that if production is increased by 1 unit, the average cost will drop by 0.3472 thousand dollars per unit or $347.2 per unit. Had they rounded one more decimal place, we would have had this number to the nearest penny.

**Problem 3** Suppose the total cost (in thousands of dollars) to produce Q units is

a. Find the the average cost of producing 40 units.

b. Find the average cost function .

c. Find the marginal average cost function .

d. Find and interpret