Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when xequalsa. c. Interpret the values obtained in part​ (b). Upper C (x )equals 0.01 x cubed plus 0.2 x squared plus 20 x plus 110​, 0less than or equalsxless than or equals1500​, aequals1000

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Answer:

[tex]C(x)=0.01x^{3} +0.2x^{2} +20x +110[/tex]

Average cost:

[tex]\frac{C(x)}{x}=\frac{0.01x^{3} +0.2x^{2} +20x +110}{x}[/tex]

[tex]=0.01x^{2} +0.2x+20+\frac{110}{x}[/tex]

Average cost at x = 1,000

[tex]=0.01(1,000)^{2} +0.2\times1,000+20+\frac{110}{1,000}[/tex]

= 10,220.11

[tex]Marginal\ cost=\frac{dC(x)}{dx}[/tex]

[tex]= 0.03x^{2} +0.4x+20[/tex]

Marginal cost at x = 1,000

[tex]= 0.03(1,000)^{2} +0.4\times1,000+20[/tex]

      = 30,420

Since marginal cost is greater than the average cost, the average cost is increasing.

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