SOLUTION: The cost (in thousands of dollars) for making x snow blowers is given by the function: C(x)= 200 + 60x The revenue (in thousands of dollars) is given by the function:

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Question 402399: The cost (in thousands of dollars) for making x snow blowers is given by the function: C(x)= 200 + 60x
The revenue (in thousands of dollars) is given by the function:
R(x)= 90x-x^2
a) write and simplify a function P that represents the profit (in thousands of dollars) in terms of x.
b) Find the number of snow blowers that would produce a zero profit.
c) What is the profit for selling 18 snow blowers?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29+=+R%28x%29+-+C%28x%29
P%28x%29+=+90x+-+x%5E2+-+%28200+%2B+60x%29
P%28x%29+=+90x+-+x%5E2+-+200+-+60x
(a)
P%28x%29+=+-x%5E2+%2B+30x+-+200
(b)
0+=+-x%5E2+%2B+30x+-+200
use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-1
b+=+30
c+=+-200
x+=+%28-30+%2B-+sqrt%28+30%5E2-4%2A%28-1%29%2A%28-200%29+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-30+%2B-+sqrt%28+900+-+800+%29%29%2F%28-2%29+
x+=+%28-30+%2B-+sqrt%28+100+%29%29%2F%28-2%29+
x+=+%28-30+%2B+10%29%2F%28-2%29+
x+=+10
and
x+=+%28-30+-+10%29%2F%28-2%29+
x+=+20
there is zero profit for selling 10 or 20 snowblowers
(c)
For selling 18 snowblowers:
P%28x%29+=+-x%5E2+%2B+30x+-+200
P%2818%29+=+-18%5E2+%2B+30%2A18+-+200
P%2818%29+=+-324+%2B+540+-+200
P%2818%29+=+16
There is $16K profit for selling 18 snowblowers
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Note that you can see the whole picture by plotting P%28x%29
+graph%28+300%2C+300%2C+-5%2C+30%2C+-5%2C+30%2C+-x%5E2+%2B+30x+-+200%29+
Note that there is no profit for selling 10 or less snowblowers
or 20 or more snowblowers