SOLUTION: Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by p(x)= -0.2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will

Algebra ->  Algebra  -> Radicals -> SOLUTION: Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by p(x)= -0.2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will      Log On

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Question 48689: Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by p(x)= -0.2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will the profit be at a maximum?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
the differential gives you a turning point on a curve, either a max or a min (or a point of inflexion).

p(x)= -0.2x^2+300x-200
p'(x)= -0.4x+300 where p'(x) is the differential
p'(x)= -0.4x+300 = 0
0.4x = 300
x = 300/0.4
x = 750

p''(x) = -0.4 which is NEGATIVE. This is therefore a MAXIMUM point.

So profit is maximised at x=750

jon.