Chapter 14, Problem 27RE

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Cost The joint cost, in dollars, for two products is given by C ( x , y ) =   x 2 y 2 +   13 . Find the marginal cost with respect to(a) x if 20 units of x and 6 units of y are produced.(b) y if 20 units of x and 6 units of y are produced.

(a)

To determine

To calculate: The marginal cost with respect to x if 20 units of x and 6 units of y are produced where the joint cost for two products is given by C(x,y)=x2y2+13.

Explanation

Given Information:

The joint cost for two products is given by C(x,y)=x2y2+13.

Also, 20 units of x and 6 units of y are produced.

Formula used:

For a joint cost function, of the form C(x,y), where x represents the quantity of product X and y represents the quantity of product Y, the marginal cost of the product X is given by âˆ‚Câˆ‚x and the marginal cost of the product Y is given by âˆ‚Câˆ‚y.

For a function f(x,y), the partial derivative of f with respect to x is calculated by taking the derivative of f(x,y) with respect to x and keeping the other variable y constant. The partial derivative of f with respect to x is denoted by fx.

Power of x rule for a real number n is such that, if f(x)=xn then fâ€²(x)=nxnâˆ’1.

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x)

(b)

To determine

To calculate: The marginal cost with respect to y if 20 units of x and 6 units of y are produced where the joint cost for two products is given by C(x,y)=x2y2+13.

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th