Concept explainers
Average Cost A clothing manufacturer finds that the cost of producing x shirts is 500 + 6x + 0.01x2 dollars.
- (a) Explain why the average cost per shirt is given by the rational expression
- (b) Complete the table by calculating the average cost per shirt for the given values of x.
x | Average cost |
10 | |
20 | |
50 | |
100 | |
200 | |
500 | |
1000 |
(a)
To explain: The average cost per shirt is given by rational expression
Explanation of Solution
The cost of producing x shirts is
The result obtained by diving the sum of all given quantities by the total number of quantities is known as average.
The average cost of one shirt is,
Thus, the average cost per shirt is given by rational expression
(b)
To find: Complete the table for average cost of shirt for different values of x.
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,
Substitute 10 for x in equation (1).
The average cost is 56.1 dollars for 10 shirts.
Substitute 20 for x into equation (1).
The average cost is 31.2 dollars for 20 shirts.
Substitute 50 for x into equation (1).
The average cost is 16.5 dollars for 50 shirts.
Substitute 100 for x into equation (1).
The average cost is 12 dollars for 100 shirts.
Substitute 200 for x into equation (1).
The average cost is 10.5 dollars for 200 shirts.
Substitute 500 for x into equation (1).
The average cost is 12 dollars for 500 shirts.
Substitute 1000 for x into equation (1).
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 |
Chapter 1 Solutions
Precalculus - A Custom Text for UNLV
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