SOLUTION: The profit P (in dollars) generated by selling x units of a certain commodity is given by P(x) = -1500 +12x-0.0004x^2 a. What is the maximum profit? B. How many units must

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The profit P (in dollars) generated by selling x units of a certain commodity is given by P(x) = -1500 +12x-0.0004x^2 a. What is the maximum profit? B. How many units must       Log On


   

Question 319919: The profit P (in dollars) generated by selling x units of a certain commodity is given by P(x) = -1500 +12x-0.0004x^2
a. What is the maximum profit?
B. How many units must be sold to generate it?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the max. value by putting the equation into vertex form,a%28x-h%29%5E2%2Bk, by completing the square.
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+P%28x%29+=-0.0004x%5E2+%2B12x-1500
P%28x%29=-0.0004%28x%5E2-30000x%29-1500
P%28x%29=-0.0004%28x%5E2-30000x%2B225000000%29-1500%2B90000
P%28x%29=-0.0004%28x-15000%29%5E2%2B88500
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The minimum occurs at the vertex.
a)Pmax=88500
b)x at Pmax:x=15000