Chapter 3.2, Problem 13E

Reminder Round all answer to two decimal places unless otherwise indicated.

Total Cost The total cost $C$ for a manufacturer during a given time period is a function of the number $N$ of items produced during that period. To determine a formula for the total cost, we need to know two things. The first is the manufacturer’s fixed costs. This amount covers expenses such as plant maintenance and insurance, and it is the same no matter how many items are produced. The second thing we need to know is the cost for each unit produced, which is called the Variable cost.

Suppose that a manufacturer of widgets has fixed costs of $\$1500$ per month and that the variable cost is $\$20$ per widget (so it costs $\$20$ to produce $1$ widget).

a. Explain why the function giving the total monthly cost $C,$ in dollars, of this widget manufacturer in terms of the number $N$ of widgets produced in a month is linear. Identify the slope and initial value of this function, and write down a formula.

b. Another widget manufacturer has a variable cost of $\$12$ per widget, and the total is $\$3100$ when $150$ widgets are produced in a month. What are the fixed costs for this manufacturer?

c. Yet another widget manufacturer has determined the following: The total cost is $\$2700$ when $100$ widgets are produced in a month, and the total cost is $\$3500$ when $150$ widgets are produced in a month. What are the fixed costs and variable costs for this manufacturer?