Profit: The background for this exercise can be found in manufacturer of widgets has fixed costs of $600 per month, and the variable cost is $60 per thousand widgets (so it costs $60 to produce a...

Profit: The background for this exercise can be found in manufacturer of widgets has fixed costs of $600 per month, and the variable cost is $60 per thousand widgets (so it costs $60 to produce a 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 = 70 − 0.03N. 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 production level at which profit is maximized if the manufacturer can produce at most 300 thousand widgets in a month.