   Chapter 11.2, Problem 4E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 1–4, for each cost function, find the marginal cost at the given production level x, and state the units of measurement. (All costs are in dollars.) [HINT: See Example 1.] C ( x ) = 20 , 000 + 50 x + 10 , 000 x ; x = 100

To determine

To calculate: The marginal cost of cost function C(x)=20000+50x+10000x dollars at the production level x=100 and state the units of measurements.

Explanation

Given Information:

The cost function is C(x)=20000+50x+10000x and the production level is x=100.

Formula used:

Sum and Difference rule of derivative, [f±g](x)=f(x)±g(x).

Constant multiple rule is f(cx)=cf(x) where c is constant.

Power rule for finding the derivative of function is, y=xn is dydx=nxn1, where n is any constant.

Derivative of constant is 0.

Calculation:

Consider the function, C(x)=20000+50x+10000x

Convert the function to power form as,

C(x)=20000+50x+10000x1

Apply sum and difference rule of derivative to the function C(x)=20000+50x+10000x with respect to x,

C(x)=ddx(20000)+ddx(50x)+ddx(10000x1)

Apply constant multiple rule

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