Thread: Help! Optimizing problems!

A net enclosure for golf practice is open at one end....( the figure is like a batting cage... a rectangle on its long side with one square shaped end open)
find the dimensions that require the least amount of netting if the volume of the enclosure is to be 250/3 cubic meters.

Originally Posted by mishmash918

A net enclosure for golf practice is open at one end....( the figure is like a batting cage... a rectangle on its long side with one square shaped end open)
find the dimensions that require the least amount of netting if the volume of the enclosure is to be 250/3 cubic meters.

Let the width be $\displaystyle w$ and the length be $\displaystyle l$ , then from what you say above the height is also $\displaystyle w$.

The area of netting is:

$\displaystyle A=w^2+3 \times (w \times l)\ \ \text{m}^2$

(one end piece of $\displaystyle w \times w$ and two sides and a top of $\displaystyle w \times l $)

Also the volume:

$\displaystyle
V=w^2 \times i=\frac{250}{3}\ \ \text{m}^3
$

Now use the last equation above to eliminate wither $\displaystyle w$ or $\displaystyle l$ from the first equation, which leaves you with an expression in a single variable for $\displaystyle A$, and you know how to find the minimum for such a problem.

CB