Question

Please Help me solve I know I am supposed to use the quadratic formula But I’m still not getting the right answers

Answer 1

To find the maximum profit we need to maximize the function.

First we need to find the critical points, to do this we need to find the derivative of the function:

`\begin{gathered} (dy)/(dx)=(d)/(dx)(-2x^2+105x-773) \\ =-4x+105 \end{gathered}`

now we equate it to zero and solve for x:

`\begin{gathered} -4x+105=0 \\ 4x=105 \\ x=(105)/(4) \end{gathered}`

hence the critical point of the function is x=105/4.

The next step is to determine if the critical point is a maximum or a minimum, to do this we find the second derivative:

`\begin{gathered} (d^2y)/(dx^2)=(d)/(dx)(-4x+105) \\ =-4 \end{gathered}`

Since the second derivative is negative for all values of x (and specially for x=105/4) we conclude that the critical point is a maximum.

Hence the function has a maximum at x=105/4. To find the value of the maximum we plug the value of x to find y:

`\begin{gathered} y=-2((105)/(4))^2+105((105)/(4))-773 \\ y=605.125 \end{gathered}`

Therefore the maximum profit is $605