SOLUTION: A printed page has 1-inch at the top and bottom, and 3/4-inch margins on each side. The area of the printed portion of the pages is 48 square inches. Find the dimension of the page

Question 1113217: A printed page has 1-inch at the top and bottom, and 3/4-inch margins on each side. The area of the printed portion of the pages is 48 square inches. Find the dimension of the page, which has the smallest possible area.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x is width, y is length of printed area
xy=48
the whole page is x+1.5 inches and y+2 inches
xy+2x+1.5y+3 has to be minimized. xy=48
2x+1.5(48/x)+51 has to be minimized
2x+(72/x)+51
Take the derivative and set equal to 0.
2-(72/x^2)=0
72=2x^2
x^2=36
x=6 inches
y=8 inches
second derivative is +144/x^3, which is positive, so the critical point is a minimum.
The page has dimensions of 7.5 x 10 or 75 in^2,
RELATED QUESTIONS
a page with length 3 inches more than its width, has 80 square inches of printed area.... (answered by ikleyn)

a page with length 3 inches more than its width, has 80 square inches of printed area.... (answered by ikleyn)

can anyone help me to find this answer?? a production editor at a textbook publishing (answered by mananth)

Please help me solve this: A page, with length 3 cm longer than its width has 80... (answered by mananth)

A page with length 3 cm longer than its width has 80 cm^2 of printed area. The margins at (answered by mananth,josgarithmetic)

Any help solving this would be GREAT!! Bob is laying out the pages of a book. Each... (answered by stanbon)

A 25-by-37-inch sheet of paper is to be used for a poster, with the shorter side at the... (answered by kitkat02)

The top and bottom margins of a rectangular poster are each 2 inches long, and the side... (answered by ankor@dixie-net.com)

Poster is to be designed with 50 in^2 of printed type, 4 inch margins on both the top and (answered by josgarithmetic)