Let's break down the questions one by one:
a. To determine the cost of producing 5,000 shoes, we can use the given cost function C(x) = 75x + 20,000. Substitute x = 5,000 into the function:
C(5,000) = 75(5,000) + 20,000
C(5,000) = 375,000 + 20,000
C(5,000) = 395,000
Therefore, the cost of producing 5,000 shoes is $395,000.
b. The cost per shoe can be found by dividing the total cost of producing 5,000 shoes by the number of shoes produced:
Cost per shoe = Total cost / Number of shoes
Cost per shoe = $395,000 / 5,000
Cost per shoe = $79
Hence, the cost of each shoe is $79.
c. The fixed cost or overhead cost of the industry is represented by the constant term in the cost function. In this case, the fixed cost is $20,000. This cost remains constant regardless of the number of shoes produced. Fixed costs include expenses like rent, insurance, and salaries that do not vary with production levels.
I hope this breakdown helps you understand how to calculate the cost of producing a specific number of shoes, the cost per shoe, and the fixed cost associated with the industry. If you have any further questions or need clarification, feel free to ask!
