   Chapter 11.2, Problem 26E 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

Housing Costs The cost C of building a house is related to the number k of carpenters used and the number x of electricians used by the formula C = 15 , 000 + 50 k 2 + 60 x 2 . a. Assuming that 10 carpenters are currently being used, find the cost function C, marginal cost function C ' , and average cost function C ¯ , all as functions of x.b. Use the functions you obtained in part (a) to compute C ' ( 15 ) and C ¯ ( 15 ) . Use these two answers to say whether the average cost is increasing or decreasing as the number of electricians increases.

(a)

To determine

To calculate: The cost function C(x), marginal cost function C'(x) and average cost function C¯(x) such that 10 carpenters are currently building a house with cost function C=15,000+50k2+60x2 where k is the number of carpenters and x is the number of electricians.

Explanation

Given Information:

Ten carpenters are currently building a house with cost function C=15,000+50k2+60x2 where k is the number of carpenters and x is the number of electricians.

Formula used:

Marginal cost is computed by the formula, Marginal cost =C(x).

Average Cost is computed by the formula, Average cost =C¯(x).

A derivative of a function y=xn using power rule is dydx=nxn1.

Sum rule of the derivative is ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)] where f(x) and g(x) are any two differentiable functions.

Constant multiple rules of the derivative are f(cx)=cf(x), where c is any constant.

A derivative of a constant is 0.

Calculation:

Consider the function,

C=15,000+50k2+60x2

As 10 carpenters are currently building a house

(b)

To determine

To calculate: The value of C(15) and C¯(15) such that 10 carpenters are currently building a house with cost function C=15,000+50k2+60x2 where k is the number of carpenters and x is the number of electricians. Also, determine whether the average cost is increasing or decreasing as electrician’s increases.

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