Question

A page that is x inches wide and y inches high contains 30 square inches of print. The top and bottom margins are 2 inches deep, and the margins on each side are 2 inches wide.
a. draw a diagram that gives a visul representation of the problem.
b. show that the total area A on the page is A=2x(2x+7)/(x-4)
c. determine the domain of the fuction based on the physical constraints of the problem.
d. use a graphing utility to graph the area function and approximate the page size for which the least amount of paper will be used.

Answer 1

if the page is x by y
then the printable area = x-4 by y-4

so (x-4)(y-4) = 30
xy -4x - 4y + 16 = 30
xy - 4y = 4x + 14
y(x-4) = (4x+14)
y = (4x+14)/(x-4)

Total area = xy
= x(4x+14)/(x-4)
= 2x(2x+7)/(x-4) ---> that would be b)

c) clearly x> 4

d) your job with the graphing utility stuff