# Word problem involving rectangle area...

• Nov 7th 2008, 04:23 AM
struck
Word problem involving rectangle area...
A rectangular sheet of metal measures 50cm by 40cm. Equal squares of side x cm are cut from each corner and discarded. The sheet is then folded up to make a tray of depth x cm. What is the domain of possible values of x? Find the value of x which maximizes the capacity of the tray.

I can handle the differentiation part. Just need the equation (Talking)
• Nov 7th 2008, 04:58 AM
earboth
Quote:

Originally Posted by struck
A rectangular sheet of metal measures 50cm by 40cm. Equal squares of side x cm are cut from each corner and discarded. The sheet is then folded up to make a tray of depth x cm. What is the domain of possible values of x? Find the value of x which maximizes the capacity of the tray.

I can handle the differentiation part. Just need the equation (Talking)

1. You can't cut off more than $20\ cm\times20\ cm-squares$ because then the width of the sheet would be zero. Therefore

$D=\{x|0\leq x \leq 20\}$

2. the volume of a prism is calculated by:

$V = (base\ area) \cdot height$

The base area is a rectangle which measures (50-2x)(40-2x)

3. Therefore the function of the volume wrt x:

$V(x)=(50-2x)(40-2x)\cdot x$