The cost of manufacturing x caseloads of ballpoint pens is dollars. How many caseloads sho...

The cost of manufacturing x caseloads of ballpoint pens is

dollars. How many caseloads should be manufactured to have an average cost of $25? [Average cost was defined in Exercise 1.]

Exercise 1

If c(x) is the cost of producing x units, then c(x)/x is the average cost per unit.* Suppose the cost of producing x units is given by c(x) = .13x3 − 70x2 + 10,000x and that no more than 300 units can be produced per week.

(a) If the average cost is $1100 per unit, how many units are being produced?

(b) What production level should be used in order to minimize the average cost per unit? What is the minimum average cost?

*Depending on the situation, a unit of production might consist of a single item or several thousand items. Similarly, the cost of x units might be measured in thousands of dollars.