Suppose that the cost, in dollars, for a company to produce x pairs of a new lin

Question

Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is cx) = 1700 + 3r + 0.01r2 + 0.0006e3 (a) Find the marginal cost function. (b) Find CT100). CT100) - what does this predict? The exact cost of the 101st pair of jeans. O The exact cost of the 90th pair of jeans. The exact cost of the 100th pair of jeans. The approoimate cost of the 100th pair of jeans. * The appeoximate cost of the 101st pair of jaans. (e) Find the difference between C(100) and the actual cost of manufacturing the 101st pair of jeans. (Round your answer to two decimal placos.) Need Help? iTesk to uber

Explanation / Answer

We have given cost C(x)=1700+3x+0.01x^2+0.0006x^3

a) Marginal cost is the derivative of the cost C(x)

C'(x)=0+3+0.02x+0.0018x^2

Marginal cost C'(x)=3+0.02x+0.0018x^2

b) We have C'(x)=3+0.02x+0.0018x^2 from part (a)

C'(100)=3+0.02*100+0.0018*(100)^2

=3+2+18

=23

C'(100)=23

This predicts the approximate cost of the 101st pair of jeans.

c) We have cost C(x)=1700+3x+0.01x^2+0.0006x^3

C(100)=1700+3*100+0.01(100)^2+0.0006(100)^3

C(100)=2700

C(101)=1700+3*101+0.01(101)^2+0.0006(101)^3

C(101)=2723.1906

the difference between C(100) and the actual cost of manufacturing the 101st pair of jeans is

C(101)-C(100)=2723.1906-2700=23.1906

the difference between C(100) and the actual cost of manufacturing the 101st pair of jeans is $23.19

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