   Chapter 11.2, Problem 23E 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

Average and Marginal Cost The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function C ( x ) = − 0.001 x 2 + 0.3 x + 500  dollars where x is the number of trinkets.a. As x increases, the marginal cost(A) increases. (B) decreases. (C) increases, then decreases.(D) decreases, then increases.b. As x increases, the average cost(A) increases. (B) decreases. (C) increases, then decreases.(D) decreases, then increases.c. The marginal cost is(A) greater than (B) equal to (C) less than the average cost when x = 100 . [HINT: See Example 4.]

(a)

To determine

The nature of marginal cost from the following options such that daily cost to manufacture trinkets is given by the function C(x)=0.001x2+0.3x+500 dollars where x means the number of trinkets increases, options are given below:

(A) increases

(B) decreases

(C) increases, then decreases

(D) decreases, then increases

Explanation

Given Information:

The daily cost to manufacture trinkets is given by the function C(x)=0.001x2+0.3x+500 dollars where x (the number of trinkets) increases. The options are as follows,

(A) increases

(B) decreases

(C) increases, then decreases

(D) decreases, then increases

Consider the function, C(x)=0.001x2+0.3x+500

As marginal cost is C'(x).

Calculate the derivative of the function with respect to x.

Apply sum rule “ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]” and constant multiple rule of derivative “f'(cx)=cf'(x)”,

C'(x)=0

(b)

To determine

The nature of average cost from the following options such that daily cost to manufacture trinkets is given by the function C(x)=0.001x2+0.3x+500 dollars where x (the number of trinkets) increases, options are given below:

(A) increases

(B) decreases

(C) increases, then decreases

(D) decreases, then increases

(c)

To determine

The relation between marginal cost and average cost when x=100 from the following options such that daily cost to manufacture trinkets is given by the function C(x)=0.001x2+0.3x+500 dollars where x (the number of trinkets) increases.

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