Question 1188918: Betty bought a snow plow for $9150. Fuel and maintenance cost 8 for each hour of use.
Find the cost function
C(x)=
If she charges $38.50 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use
R(x)=
Find the profit function P(x) for the amount gained from x hours of use
P(x)=
How many hours will she need to break even?
I am confused on this question
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of hours of use.
cost = 9150 + 8 * x = c(x).
revenue = 38.5 * x = r(x).
profit = p(x) = r(x) - c(x)
she will break even when p(x) = 0.
that means she neither makes a profit nor takes a loss.
youe equation is:
p(x) = r(x) - c(x)
when p(x) = 0, the equation becomes:
0 = r(x) - c(x)
since r(x) = 38.5 * x and c(x) = 9150 + 8 * x, the equation becomes:
0 = 38.5 * x - (9150 + 8 * x
simplify by removing parentheses to get:
0 = 38.5 * x - 9150 - 8 * x
combine like terms to get:
0 = 30.5 * x - 9150
add 9150 to both sides of the equation to get:
9150 = 30.5 * x
divide both sides by 30.5 to get:
9150 / 30.5 = x
solve for x to get:
x = 300
she will need to work 300 hours to break even.
r(x) = 38.5 * 300 = 11,550
c(x) = 9150 + 8 * 300 = 11,550
p(x) = r(x) - c(x) = 0
if she works more than 300 hours, r(x) will be positive and she will make a profit.
if she works less than 300 hours, r(x) will be negative and she will take a loss.
break even is when you neither take a profit nor take a loss.
let me know if you have any questions.
theo
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