Help with a math problem! Finding break even points.?
A sporting goods store finds that if it sells x exercise machines per day, then its costs will be
C(x) = 80x + 8000
and its revenue will be
R(x) = −2x2 + 360x
(both in dollars).
(a) Find the store s break-even points.
(b) Find the number of sales that will maximize profit, and find the maximum profit.
- TomVLv 76 months ago
a) Break even point is where cost and revenue are equal.
C(x) = R(x)
80x + 8000 = -2x² + 360x
2x² - 280x + 8000 = 0
x² - 140x + 4000 = 0
(x-40)(x-100) = 0
x = 40, 100
Break even points are sales of 40 or 100 machines per day.
b) Profit is Revenue minus cost.
P(x) = R(x) - C(x)
P(x) = -2x² + 360x - 80x - 8000
= -2x² + 280x - 8000
dP/dx = - 4x + 280 = 0
x = 70
P(70) = -2(70)² + 280(70) - 8000 = 1800
Maximum profit of $1800 per day occurs at 70 sales per day.
- Anonymous6 months ago
start by graphing both functions