# Math Help - Maximizing and minimizing

1. ## Maximizing and minimizing

Hi, I've got 3 problems that I'm really stuck on, but I'll post the first one.
Any help MUCH appreciated because the assignment is due in about 14 hours.

1. Maximize P=xyz with x+z=12, y+z=12, and x,y,and z >=0
The farthest I got on this one was to rearrange the variables to make z the only unknown, then taking the derivative, but I'm stuck from there.

the last part I have written on it is 16z+z^2 = 48

2. Originally Posted by leviathanwave
Hi, I've got 3 problems that I'm really stuck on, but I'll post the first one.
Any help MUCH appreciated because the assignment is due in about 14 hours.

1. Maximize P=xyz with x+z=12, y+z=12, and x,y,and z >=0
The farthest I got on this one was to rearrange the variables to make z the only unknown, then taking the derivative, but I'm stuck from there.

the last part I have written on it is 16z+z^2 = 48
that equation is wrong. after substituting for x and y and differentiating and setting the derivative to zero, you should end up with: $z^2 -16z + 48 = 0$

now just find the vertex of that. (for the vertex, $z = \frac {-b}{2a}$, where a is the coefficient of $z^2$ and b is the coefficient of z)

3. oh so I don't have to use the quadratic formula?

4. Originally Posted by leviathanwave
oh so I don't have to use the quadratic formula?
no, we use the quadratic formula to solve for the zeros of a quadratic. you don't want the zeros, you want the vertex