Q. 116 - Precalculus Enhanced with Graphing Utilities

Question

The fixed costs of operating a business are the costs incurred regardless of the level of production. Fixed costs include rent, fixed salaries, and costs of leasing machinery. The variable costs of operating a business are the costs that change with the level of output. Variable costs include raw materials, hourly wages, and electricity. Suppose that a manufacturer of jeans has fixed daily costs of \(500 and variable costs of \)8 for each pair of jeans manufactured. Write a linear equation that relates the daily cost C, in dollars, of manufacturing the jeans to the number x of jeans manufactured. What is the cost of manufacturing 400 pairs of jeans? 740 pairs?

Step-by-Step Solution

Answer

• The linear equation that relates the daily cost C, in dollars, of manufacturing the jeans to the number $x$ of jeans manufactured: $C=8x+500$
• The cost of manufacturing 400 pairs of jeans is: $\$3700$
• The cost of manufacturing 740 pairs of jeans is: $\$6420$

Step 1. Given information

A manufacturer of jeans has fixed daily costs of $500 and variable costs of $8 for each pair of jeans manufactured.

Step 2. Required to find

• Write a linear equation that relates the daily cost C, in dollars, of manufacturing the jeans to the number x of jeans manufactured. 
• What is the cost of manufacturing 400 pairs of jeans.
• What is the cost of manufacturing 740 pairs of jeans.

Step 3. Finding the linear equation

The required equation is: $C=8x+500$

Step 4. Finding the cost of manufacturing jeans

Cost of manufacturing 400 pairs of jeans

Put $x=400$ in above linear equation

$C=8\times 400+500$

$C=3200+500$

$C=3700$

Cost of manufacturing 740 pairs of jeans

Put $x=740$ in above linear equation

$C=8\times 740+500$

$C=5920+500$

$C=6420$