A rectangular poster is to contain 81 square inches of print. The margins at the top and bottom and on each side are to be 5 inches. Find the dimensions of the page which will minimize the amount of paper used.

lenght 19 in

width 19 in

Step-by-step explanation:

Let x and y be dimensions of print area, that is

x*y = 81 in² then y = 81/x

then total area of the poster is (including top, bottom and sides margins)

(x + 10) * (y + 10) = A (t)

A (x) = (x + 10) * (81/x + 10) solving

A (x) = 81 + 10x + 810/x + 100

Taking derivatives both sides of the equation

A' (x) = 10 - 810/x²

A' (x) = 0 10 - 810/x² = 0 (10x²-810) / x² = 0

10x² - 810 = 0

x² = 81

x = 9 in then y = 81/x y = 81/9 y = 9 in

Then remember, these are values for the print area, now we have to add 10 inches according to margins

The dimensions of the poster will be

lenght 19 in

width 19 in