The fixed costs of oreparting a business are the costs include rent, fixed salaries, and costs of buying machinery. The variable costs of operating a business are the costs that change with the level of ouput. Variable costs include raw materials, hourly wages, and electricity. Suppose that a manufacturer of jeans has fixed costs of $500 and variable costs of $8 for ech pair of jeans manufactured. Write a linear equation that relates the cost C, in dollars of manufacuting the jeans to the number x of pairs of jeans manufactured. What is the cost of manufacturing 400 pairs of jeans? 740 pairs?
To write a linear equation that relates the cost C, in dollars of manufacturing the jeans, to the number x of pairs of jeans manufactured, we need to consider both the fixed costs and the variable costs.
The fixed costs are constant and do not change with the level of output. In this case, the fixed costs are $500.
The variable costs, on the other hand, change with the level of output, and in this case, it is $8 for each pair of jeans manufactured.
So, the linear equation that relates the cost C to the number x of pairs of jeans manufactured can be written as:
C = fixed costs + (variable costs * x)
Substituting the values, the equation becomes:
C = 500 + (8 * x)
Now, to find the cost of manufacturing 400 pairs of jeans, we substitute x with 400 in the equation:
C = 500 + (8 * 400)
C = 500 + 3200
C = 3700
Therefore, the cost of manufacturing 400 pairs of jeans is $3700.
Similarly, to find the cost of manufacturing 740 pairs of jeans, we substitute x with 740 in the equation:
C = 500 + (8 * 740)
C = 500 + 5920
C = 6420
Therefore, the cost of manufacturing 740 pairs of jeans is $6420.