Total revenue and profit: This is a continuation . The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. In this...

Total revenue and profit: This is a continuation . The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. In this exercise we assume that the selling price per unit of the item is a constant, so it does not depend on the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. If the profit is zero, then the manufacturer is at a break-even point. We consider again the manufacturer of widgets with fixed costs of $1500 per month and a variable cost of $20 per widget. Suppose the manufacturer sells 100 widgets for $2300 total.

a. Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.

b. Use a formula to express the monthly profit P , in dollars, of this manufacturer as a function of the number of widgets produced in a month. Explain how the slope and initial value of P are derived from the fixed costs, variable cost, and price per widget.

c. What is the break-even point for this manufacturer?

d. Make graphs of total monthly cost and total monthly revenue. Include monthly production levels up to 1200 widgets. What is the significance of the point where the graphs cross?