Question

A printer needs of make a poster that
will have a total area of 200 inch and
well have 1 inch margin on the side, a
2 inch margin on the top and a 1.5
inch margin at the bottom. What
dimension of the poster will give the
largest printed area?​

Answer 1

Here is ur answers

let x = length of the full poster

then 200/x = width of the full poster

so

length of the printed area is x - 3.5

and width of the printed area is (200/x)-2

so

Area of Printed space = (x-3.5)((200/x)-2)

take the derivative using the product rule

A' = (x-3.5)(-200/x2) + ((200/x)-2)

A' = 700 -2x2 (you can fill in the steps - I got lazy)

now set the derivative to o

0 = 700 -2x2

700 = 2x2

350 = x2

x = 18.70829 The original length

width = 10.69045

area of space available for printing is

15.20829 * 8.69045

= 132.1669 sq in