# Math Help - More Optimization Problems

1. ## More Optimization Problems

1. Find the minimum value of A if A=4y + x^2, where (x^2 + 1)y=324.

2. By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. If the cardboard is 16 inches long and 10 inches wide, find the dimensions of the box that will yield maximum volume

2. $\begin{gathered}
A(x,y) = 4y + x^2 \hfill \\
\quad y(x^2 + 1) = 324 \hfill \\
\end{gathered}
$

now just plug the constraint into the equation:

$
A = 4\frac{{324}}
{{x^2 + 1}} + x^2
$

differentiate with respect to x...

2. $
v = \left( {10 - 2x} \right)\left( {16 - 2x} \right)x
$