Question

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

Answer 1

Call x and y are width and length of print area. Thus xy = 24, or y = 24/x
The area of paper is
P(x) = (x + 2)(24/x +3) = 24 + 3x + 48/x + 6 = 30 + 3x + 48/x
P'(x) = 3 - 48/x^2
Extrema occur when derivative = 0, or
3 - 48/x^2 = 0
48/x^2 = 3
x^2 = 16
x = +- 4
P(x) is minimum when x = 4
The dimensions of the print area is 4 x 6
The dimensions of the paper is 6 x 9

Answer 2

Thank you!

Answer 3

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