A rectangular page is to contain 24 square

Answered question

2022-02-24

A rectangular page is to contain 24 square inches of print. The margins at the top and the bottom of the page are 1.5 inches, and the margins on the left and the right are 1 inch. What should be the measure of the page for the least amount of paper?

Answer & Explanation

alenahelenash

alenahelenash

Expert2022-03-10Added 556 answers

Let's say that x is the width of the print on the page, and that yis the height of the print on the page.
xy=24
x=24y
A page =(x+2)(y+3)=xy+3x+2y+6.
Substituting, we put x=24y.
A page =24+72y+2y+6.
Taking the derivative and setting it equal to 0,
A page =272y2=0
2y2=72
y2=36
y=6
Setting x=24y, we find x is 4.
So, the dimensions of the page are (6+2)=8, and (4+3)=7
8 in, by 7 in.

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