The cost, in dollars, of producing x yards of a certain fabric is C ( x ) = 1400

Question

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

C(x) = 1400 + 14x 0.1x^2 + 0.0005x^3.

(a) Find the marginal cost function.
C'(x) = 140.2x+0.0014x^2

(b) Find C'(200) and explain its meaning. What does it predict?

C'(200) = __________________

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

x = __________  . C'(200) predicts the cost of producing the 201st

(c) Compare C'(200) with the cost of manufacturing the 201st yard of fabric. (Round your answers to four decimal places.)The cost of manufacturing the 201st yard of fabric is

C(201) C(200) =__________________________ 4,200 _________________________ ,

which is approximately

C'(200).

Explanation / Answer

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

C(x) = 1400 + 14x 0.1x2 + 0.0005x3.

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

(b) Find

C'(200) =14 0.2*(200) + 0.0015(200)2 =34

and explain its meaning. What does it predict?

cost of producing additional unit after producing 200 units is 34

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

x =200 .

predicts the cost of producing the 201th

yard.

(c) Compare

C'(200)

with the cost of manufacturing the 201st yard of fabric. (Round your answers to four decimal places.)The cost of manufacturing the 201st yard of fabric is

C(201) C(200) = (1400 + 14*201 0.1*(201)2 + 0.0005*(201)3.)- (1400 + 14*200 0.1*(200)2 + 0.0005*(200)3.) =4234.2005-4200

=34.2005

which is approximately =34.2

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