Bea T. Howen, a sophomore college student, lost her scholarship after receiving a D in her "Music Appreciation" course. She decided to buy a snow plow to supplement her income during the winter months. It cost her $5550.00. Fuel and standard maintenance will cost her an additional $8.25 for each hour of use..
(a) Find the cost function C(x) associated with operating the snow plow for x hours.
If she charges $36.00 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use.
(b) Find the profit function P(x) for the amount of profit gained from x hours of use.
How many hours will she need to work to break even?

(a) Howen's costs include fixed costs and a cost per hour. Then her total cost will be the sum of the fixed cost (5550) and the product of hours (x) and the cost per hour (8.25):

C(x) = 5550 +8.25x

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(b) Howen plans to charge a given amount (36) per hour, so her revenue will be the product of that amount and the number of hours she works:

R(x) = 36x

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(c) Her profit function is the difference between revenue and cost:

P(x) = R(x) -C(x)

P(x) = 36x -(5550 +8.25x)

P(x) = 27.75x -5550

Howen's break-even point is the number of hours required to make profit be zero:

0 = 27.75x -5550

0 = x - 200 . . . . . . . . . divide by 27.75

200 = x . . . . . . . . . . . . add 200

She needs to work 200 hours to break even.