# A rectangular page contains 64 square inches of point. The margins at the top and bottom of the page are each 3 inches deep. The margins on each side are 1 1/2 inches wide. What should the dimensions of the page to use the least amount of paper?

A rectangular page contains 64 square inches of print. The marginis at the top and bottom of the page are each 3 inches deep. The margins on each side are $1\frac{1}{2}$ inches wide. What should the dimensions of the page be to use the least amount of paper?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

mercuross8
Let, x bet the width of the print then the width of the page $\left(x+2\left(1\frac{1}{2}\right)\right)=x+3$
Also, let y be the height of the prinbt. Then, the height of the page is $\left(y+2\left(3\right)\right)\phantom{\rule{0ex}{0ex}}=y+6$
Now, the area of the print is 64 square inches so, $xy=64\phantom{\rule{0ex}{0ex}}y=\frac{64}{x}$
The area of the page
$A=\left(x+3\right)\left(y+6\right)\phantom{\rule{0ex}{0ex}}=\left(x+3\right)\left(\frac{64}{x}+6\right)$
Minimum area occyrs when
Hence, $y=\frac{64}{4\sqrt{2}}\cong 11.3$
###### Not exactly what you’re looking for?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee