708 CHAPTER 9 THE DERIVATIVE 9.8 Exercises 1. PRODUCTION COSTS The graph of a ty

Question

708 CHAPTER 9 THE DERIVATIVE 9.8 Exercises 1. PRODUCTION COSTS The graph of a typical total cost func- tion C(x) associated with the manufacture of x units of a certain commodity is shown in the figure. a. Explain why the function C is always increasing. b. As the level of production x increases, the cost per unit drops so that C(x) increases but at a slower pace. However, a level of production is soon reached at which the cost per unit begins to increase dramatically (owing to a shortage of raw material, overtime, break- down of machinery due to excessive stress and strain), so C(x) continues to increase at a faster pace. Use the graph of C to find the approximate level of production o where this occurs. y C(x) x (thousands)

Explanation / Answer

a)

C is always increasing because producing more units is going to cost more ie if x<y

Then cost of producing y units is going to be more than producing x units though the cost per unit may be lower

b)

We are looking for the point where graph turns from concave down to concave up.

We see from the graph it is at around x=3

So x0~3

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