A rectangular page is to contain 145 square inches of print. The top and bottom margins are each 0.9 inches wide , and the margins on each side is 1.75 inches wide. What should the dimensions be if the least amount of material is to be used ?

Question

anonymous · Answer

Let x by the top and bottom of print and let y be the sides of print. then xy=145 to get 145 square inches of print (so, y=145/x). The material used is x+2(.09)=x+.18 for the top and bottom and y+2(1.75)=y+3.5 for the sides. So, the area is:

A(x)=(x+.18)(y+3.5) 

Multiply out, take the derivative, set it equal to zero, and solve for x, then solve for y: