Profit: The background for this exercise can be found in manufacturer of widgets has fixed costs of $150 per month, and the variable cost is $50 per widget (so it costs $50 to produce 1 widget). Let N...

Profit: The background for this exercise can be found in manufacturer of widgets has fixed costs of $150 per month, and the variable cost is $50 per widget (so it costs $50 to produce 1 widget). Let N be the number of widgets produced in a month.

a. Find a formula for the manufacturer’s total cost C as a function of N.

b. The manufacturer sells the widgets for $65 each. Find a formula for the total revenue R as a function of N.

c. Use your answers to parts a and b to find a formula for the profit P of this manufacturer as a function of N.

d. Use your formula from part c to determine the break-even point for this manufacturer.