SOLUTION: A rectangular page is to be used to contain 24 square inches of print. The top and bottom margins are 1.5 inches wide. The left and right side margins are 1 inch wide. What should

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Question 1078551: A rectangular page is to be used to contain 24 square inches of print. The top and bottom margins are 1.5 inches wide. The left and right side margins are 1 inch wide. What should the dimensions of the page be so that the least amount of paper is used?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= width of the printed part, in inches
y= height of the printed part, in inches
xy=24= area of the printed part, in square inches
So, y=24%2Fx
x%2B2%2A1=x%2B2= width of the page, in inches
y%2B2%2A1.5=y%2B3= height of the page, in inches
The area of the page (in square inches) is
A=%28x%2B2%29%28y%2B3%29=xy%2B3x%2B2y%2B6=24%2B3x%2B2%2824%2Fx%29%2B6=3x%2B48%2Fx%2B30
One way to d=find the minimum is
to calculate the derivative dA%2Fdx ,
and solve the equation dA%2Fdx=0 .
dA%2Fdx+=3-48%2Fx%5E2=%283x%5E2-48%29%2Fx%5E2=3%28x%5E2-16%29%2Fx=3x-4x%2B4%2Fx2
dA%2Fdx=0 ---> x=4 ,
The width and height of the paper are
x%2B2=4%2B2=6 and
y%2B3=24%2Fx%2B3=48%2F4%2B3=6%2B3=9 .
The dimensions of the page, so that the least amount of paper is used
must be 6 inches wide by 9 inches tall.