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

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) (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.

RELATED QUESTIONS
Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given... (answered by fractalier)

Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given... (answered by josmiceli)

The total profit (in dollars) for sales of x rowing machines is given by... (answered by funmath)

The total profit (in dollars) for sales of x rowing machines is given by... (answered by ankor@dixie-net.com)

I need a little help with this one please: Maximizing profit. The total profit (in... (answered by jake_6233)

The total profit (in dollars) for sales of x rowing machines is given by P(x) = 0.2 x^2 + (answered by rapaljer)

I am needing help solving this word problem- these are too confusing to me The total... (answered by richwmiller)

114. Surface area of a cube. The formula A =6V^2/3 gives the surface area of a cube in... (answered by Alan3354,ankor@dixie-net.com)

114. Surface area of a cube. The formula A =6V^2/3 gives the surface area of a cube in... (answered by edjones)