The cost, in dollars, of producing x yards of a certain fabric is C ( x ) = 1500

Question

The cost, in dollars, of producing x yards of a certain fabric is

C(x) = 1500 + 14x 0.1x2 + 0.0005x3.

(a) Find the marginal cost function.

(b) Find

C'(300)

and explain its meaning. What does it predict?

C'(300) =

and this is the rate at which costs are increasing with respect to the production level when

x = . C'(300)

predicts the cost of producing the

yard.

(c) Compare

C'(300)

with the cost of manufacturing the 301st yard of fabric. (Round your answers to four decimal places.)The cost of manufacturing the 301st yard of fabric is

C(301) C(300) = 10,200

which is approximately

C'(300).

Explanation / Answer

The cost, in dollars, of producing x yards of a certain fabric is

C(x) = 1500 + 14x 0.1x2 + 0.0005x3.

(a) Find the marginal cost function. dC/dx =14 0.2x + 0.0015x2.

(b) Find

C'(300) =14 0.2*(300) + 0.0015(300)2 =89

and explain its meaning. What does it predict?

cost of producing additional unit after producing 300 units is 89

and this is the rate at which costs are increasing with respect to the production level when

x =300 .

predicts the cost of producing the 301th

yard.

(c) Compare

C'(300)

with the cost of manufacturing the 301st yard of fabric. (Round your answers to four decimal places.)The cost of manufacturing the 301st yard of fabric is

C(301) C(300) = (1500 + 14*301 0.1*(301)2 + 0.0005*(301)3.)- (1500 + 14*301 0.1*(301)2 + 0.0005*(301)3.) =10289.35-10200

=89.35

which is approximately =89

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