SOLUTION: a company manufactures and sells t-shirts. the marketing department estimates that if they sell 'n' units (in thousands) the weekly cost c(x) and the revenue r(x) (in thousands of

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Question 1087419: a company manufactures and sells t-shirts. the marketing department estimates that if they sell 'n' units (in thousands) the weekly cost c(x) and the revenue r(x) (in thousands of dollars) will be given by the equations
r(x)= -4x^3+20x^2-25
C(x)= 6x^2-14x+35
determine the number of t-shirts for which the company will make a profit.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that n=x,
Find the breakeven point,
R%28x%29=C%28x%29
-4x%5E3%2B20x%5E2-25=6x%5E2-14x%2B35
-4x%5E3%2B14x%5E2%2B14x-60=0
You can factor,
-2%28x-3%29%28x%2B2%29%282x-5%29=0
Only positive solutions make sense.
In order the first positive zero would be,
2x-5=0
2x=5
x=5%2F2
So making more than 2,500 t-shirts would be profitable.
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