A manufacturer finds that the profit P from assembling x bicycles per day is given by
P(x) = -x^2 + 50x - 200
What is the maximum profit?
I figured to find the max profit i should find the turning point of of the parabola which illustrates this equation.
What I got was (25, 1675)
So I figured that it would be $1675
HOWEVER, the answer says 425 dollars!
Could you tell me how to do this?
P(x) = y = -x^2 + 50x - 200,
x^2 - 50x +200 = -y
completing the square,
x^2 - 50x +(-50/2)^2 = -y +(-50/2)^2 - 200
(x - 25)^2 = -(y - 425)
(x,y) --> (25, 425), the value of x and y are the maximum that can be obtained, its the apex of the inverted parabola
x = units,
y = P(x) = $425.00, profit in dollars
the graph below confirms the answer.