SOLUTION: Hello! I am needing help on a word problem. Macro Manufacturing estimates that its profit P in hundreds of dollars is P= -2x^2 + 20x-2 where x is the number of units produced

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Question 383959: Hello! I am needing help on a word problem.
Macro Manufacturing estimates that its profit P in hundreds of dollars is P= -2x^2 + 20x-2 where x is the number of units produced in thousands. How many units must be produced to obtain maximum profit?
Thanks so much!
Denise
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the max or min for a quadratic equation, convert to vertex form (y=a%28x-h%29%5E2%2Bk) by completing the square.
P=+-2x%5E2+%2B+20x-2
P=-2%28x%5E2-10x%29-2
P=-2%28x%5E2-10x%2B25%29-2%2B2%2825%29
P=-2%28x-5%29%5E2-2%2B50
P=-2%28x-5%29%5E2%2B48
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The vertex is (5,48), with a maximum profit of 48 hundred dollars which occurs when x=5 thousand units are produced.
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