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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Marginal Cost A company manufactures mountain bikes and racing bikes. The cost function for producing x mountain bikes and y racing bikes is given by

C = 10 x y + 149 x + 189 y + 675.

(a) Find the marginal costs (∂C/∂x and ∂C/∂y) when x = 120 and y = 160.

(b) When additional production is required, which model of bicycle results in the cost increasing at a higher rate? How can this be determined from the cost model?

(a)

To determine

To calculate: The marginal cost Cx and Cy at the point x=120 and y=160 if a company manufactures mountain bikes and racing bikes, the cost function for producing bikes can be modeled by C=10xy+149x+189y+675.

Explanation

Given information:

A company manufactures mountain bikes and racing bikes, the cost function for producing bikes can be modeled by C=10xy+149x+189y+675. Where, x represent maintains bikes and y racing bikes.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided cost function is,

C=10xy+149x+189y+675

Partially derivative of the function C=10xy+149x+189y+675 with respect to x.

Cx=x(10xy+149x+189y+675)=10x(xy)+149x(x)+189yx(1)+675x(1)=10y2x(1)+149=5yx+149

Now, substitute x=120 and y=160 in the marginal cost Cx=5yx+149.

(Cx)(120,160)=5160120+149=5423+1495

(b)

To determine

The model of bikes was used when the additional production is required for cost increasing at higher rate.

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