A manufacturer of widgets has fixed costs of $680 per month, and the variable cost is $66 per thousand widgets (so it costs $66 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.

C(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.

R(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.

P(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. (Round your answers to two decimal places.)

_______ thousand widgets per month (smaller value)

_______ thousand widgets per month (larger value)