Breaking even: The background for this exercise can be found in A manufacturer of widgets has fixed costs of $700 per month, and the variable cost is $65 per thousand widgets (so it costs $65 to...

Breaking even: The background for this exercise can be found in A manufacturer of widgets has fixed costs of $700 per month, and the variable cost is $65 per thousand widgets (so it costs $65 to produce 1 thousand widgets). Let N be the number, in thousands, of widgets produced in a month.

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

b. The highest price p,in dollars per thousand widgets, at which N can be sold is given by the formula p = 75 − 0.02N. Using this, 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 two break-even points for this manufacturer.Assume that the manufacturer can produce at most 500 thousand widgets in a month.