SOLUTION: The cost and revenue functions for selling a specialty item are:
R(x) = 50x – 0.5 x2
C(x) = 4x + 10x2
a) Write the equation of the profit function P(x).
b) Sketch th
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Question 631903: The cost and revenue functions for selling a specialty item are:
R(x) = 50x – 0.5 x2
C(x) = 4x + 10x2
a) Write the equation of the profit function P(x).
b) Sketch the three functions C(x), R(x) and P(x) on the same set of axis.
c) Determine the number of specialty items which produce a maximum profit.
d) Find the maximum profit.
e) Indicate on the profit curve the interval over which profit is decreasing.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Profit is Revenue minus Cost, so:
\ =\ R(x)\ -\ C(x)\ =\ \left(50x\ -\ 0.5x^2\right)\ -\ \left(4x\ +\ 10x^2\right))
I'll lead the simplification and the graphing to you.
The profit function is a parabola that opens down. The answer to part c is the value of the 
coordinate of the vertex, and the answer to d is the 
coordinate of the vertex.
John
My calculator said it, I believe it, that settles it
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