SOLUTION: The profit in terms of number of units x produced is given by P(x)=-x^3/3+729-25000. The value of x that maximizes the profit is : ?

Algebra ->  Finance -> SOLUTION: The profit in terms of number of units x produced is given by P(x)=-x^3/3+729-25000. The value of x that maximizes the profit is : ?      Log On


   

Question 1001447: The profit in terms of number of units x produced is given by P(x)=-x^3/3+729-25000. The value of x that maximizes the profit is : ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think you have an error in your equation.
As written it has no maximum value so I'm assuming it's quadratic.
Complete the square to put in vertex form and the maximum occurs at the vertex.
P%28x%29=-x%5E2%2F3%2B729x-25000
P%28x%29=-%281%2F3%29%28x%5E2-2187x%29-25000

P%28x%29=-%281%2F3%29%28x-2187%2F2%29%5E2-3000000%2F12%2B4782969%2F12
P%28x%29=-%281%2F3%29%28x-2187%2F2%29%5E2%2B4482969%2F12
P%28x%29=-%281%2F3%29%28x-2187%2F2%29%5E2%2B1494323%2F4
So the maximum profit of 373580.75 occurs at x=2187%2F2=1093.5
In terms of units, you can only make integer values of units so you would make either 1093 or 1094.