Suppose that the t cost function, in dollars, for the production ofx units of a

Question

Suppose that the t cost function, in dollars, for the production ofx units of a product is aiven by the equation shown below. c() 18050 50x 0.5x? Then the average cost of producing x items is represented by the following equation. total cost 18050 x) 50 0.5x (a) Find the instantaneous rate of cange of average cost with respect to the number of units produced at any level of production. en- (b) Find the level of production at which this rate of change equals zero. (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost instantaneous rate of change of cost average cost What do you notice? O The instantaneous rate of change of cost equals the average cost. O The instantaneous rate of change of cost is greater than the average cost. O The instantaneous rate of change of cost is less than the average cost.

Explanation / Answer

a)

-18050/x^2 + 0.5

b)

-18050/x^2 + 0.5 = 0

18050/x^2 = 0.5

x^2 = 18050/0.5

x^2 = 36100

x = 190 ---> ANSWER

c)

C = 18050 + 50x + 0.5x^2

So, dC/dx = 50 + x = 50 + 190 = 240 --> first blank

Average cost = 18050/190 + 50 + 0.5*190 = 240 --> second blank

What do you notice :

The inst rate of change of cost equals the average cost

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