Question 219464: Can someone explain to me how this is done:
Profit = -0.25Q^2 + 10Q - 4
Profit = -0.25(Q^2-40Q) - 4
Profit = -0.25 (Q^2-40Q +400) - 4 +100
Profit = -0.25(Q-20)^2 + 96 Therefore Profit(max) = 96 @ Q = 20
How do you get 40Q?
How do you get 400?
How do you get (Q-20)?
Also - is this algebra? Since I do not understand the rules here on how to work through this problem, what should I be studying here?
Thanks, SJ
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Can someone explain to me how this is done:
Profit = -0.25Q^2 + 10Q - 4
Factoring out -0.25 from the 1st two terms you get:
Profit = -0.25(Q^2-40Q) - 4
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Completing the square on the Q-terms you get:
Profit = -0.25 (Q^2-40Q +400) - 4 +100
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Writing the factored form of Q^2-40Q+400 you get:
Profit = -0.25(Q-20)^2 + 96
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Therefore Profit(max) = 96 @ Q = 20
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How do you get 40Q?
How do you get 400?
How do you get (Q-20)?
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Also - is this algebra?
Yes. You would need to learn "solving quadratic equations by completing
the square", which is usually taught in Algebra II.
Cheers,
Stan H.
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