BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.4, Problem 102E

(a)

To determine

To explain: The average cost per shirt is given by rational expression A=500+6x+0.01x .

Expert Solution

Explanation of Solution

The cost of producing x shirts is 500+6x+0.01x2 .

The result obtained by diving the sum of all given quantities by the total number of quantities is known as average.

Avearge=SumofallquantitiesNumberofquantities

The average cost of one shirt is,

Averagecost=500+6x+0.01x2x

Thus, the average cost per shirt is given by rational expression A=500+6x+0.01x .

(b)

To determine

To find: Complete the table for average cost of shirt for different values of x.

Expert Solution

Answer to Problem 102E

The table for average cost per shirt for different value of x is,

x Average Cost
10 56.1
20 31.2
50 16.5
100 12
200 10.5
500 12
1000 16.5

Explanation of Solution

Given:

The different values of x are 10, 20, 50, 100, 200, 500 and 1000.

Calculation:

From part (a), the average cost per shirt is,

A=500+6x+0.01x2x (1)

Substitute 10 for x in equation (1).

A=500+6(10)+0.01(10)210=500+60+110=56110=56.1

The average cost is 56.1 dollars for 10 shirts.

Substitute 20 for x into equation (1).

A=500+6(20)+0.01(20)220=500+120+420=62420=31.2

The average cost is 31.2 dollars for 20 shirts.

Substitute 50 for x into equation (1).

A=500+6(50)+0.01(50)250=500+300+2550=82550=16.5

The average cost is 16.5 dollars for 50 shirts.

Substitute 100 for x into equation (1).

A=500+6(100)+0.01(100)2100=500+600+100100=1200100=12

The average cost is 12 dollars for 100 shirts.

Substitute 200 for x into equation (1).

A=500+6(200)+0.01(200)2200=500+1200+400200=2100200=10.5

The average cost is 10.5 dollars for 200 shirts.

Substitute 500 for x into equation (1).

A=500+6(500)+0.01(500)2500=500+3000+2500500=6000500=12

The average cost is 12 dollars for 500 shirts.

Substitute 1000 for x into equation (1).

A=500+6(1000)+0.01(1000)21000=500+6000+100001000=165001000=16.5

The average cost is 16.5 dollars for 1000 shirts.

Thus, the table for average cost per shirt for different value of x is,

x Average Cost
10 56.1
20 31.2
50 16.5
100 12
200 10.5
500 12
1000 16.5

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