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?

souta5 2022-09-12 Answered
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 1 2 inches wide. What should the dimensions of the page be to use the least amount of paper?
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Answers (1)

mercuross8
Answered 2022-09-13 Author has 16 answers
Let, x bet the width of the print then the width of the page ( x + 2 ( 1 1 2 ) ) = x + 3
Also, let y be the height of the prinbt. Then, the height of the page is ( y + 2 ( 3 ) ) = y + 6
Now, the area of the print is 64 square inches so, x y = 64 y = 64 x
The area of the page
A = ( x + 3 ) ( y + 6 ) = ( x + 3 ) ( 64 x + 6 )
Minimum area occyrs when d A d x = 0 or,  64 x + 6 + ( x + 3 ) ( 64 x 2 ) = 0 or,  x = + 4 2 5.7
Hence, y = 64 4 2 11.3
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