Bea T Howen a sophomore college student lost her scholarship

Bea T. Howen, a sophomore college student, lost her scholarship after receiving a D in her \"music appreciation\" course. She decided to buy a show plow to supplement her income during the winter months. It cost her $5800.00 fuel and standard maintenance will cost her an additional $8.00 for each hour of use. Find the cost function C(x) associated with operating the show plow for x hours. It she charges $37.00 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use 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 t break even?

Solution

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Given fixed cost = 5800$

Variable Cost (Fuel & Maintainence) = 8$/hour

C(x) = 5800 + 8x where x is the number of hours

Revenue charged = R(x) = 37x

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

P(x) = 37x - 5800 - 8x

P(x) = 29x - 5800

Breakeven point is achieved when P(x) = 0

29x - 5800 = 0

x = 200 hours Solution