Question

MANUFACTURING COST A manufacturer's total cost consists of a fixed overhead of $5,000 plus production costs of $60 per unit.

a. Express the total cost as a function of the number of units produced, and sketch its graph.
b. Find the average cost function AC(x). What is the average cost of producing 20 units?

Answer 1

The total cost can be expressed as TC(x) = $5,000 + $60x. The average cost function is AC(x) = ($5,000 + $60x) / x. To find the average cost of producing 20 units, substitute x = 20 into AC(x) equation.

Step-by-step explanation:

To express the total cost as a function of the number of units produced, we add the fixed overhead of $5,000 to the production costs of $60 per unit. Let x represent the number of units produced. The total cost (TC) can be expressed as TC(x) = $5,000 + $60x. To sketch the graph, plot the quantity (x) on the x-axis and the total cost (TC) on the y-axis. The graph will be a straight line with a positive slope of $60.

To find the average cost function (AC(x)), we divide the total cost (TC) by the number of units produced (x). AC(x) = TC(x) / x. Substituting the expression for TC(x), we get AC(x) = ($5,000 + $60x) / x. To find the average cost of producing 20 units, we substitute x = 20 into the AC(x) equation and solve for AC(20).