Question

A printer need to make a poster that will have a total poster area of 200 in^2 and will have 1 inch margins on the sides, a 2-inch margins on both the top and the bottom. What dimensions will give the largest printed area?

Answer 1

Answer:

The dimensions that will give the largest printed area of 132.1669 in^2 are

= Length x Width

= 15.20829 * 8.69045

Step-by-step explanation:

a) Data and Calculations:

Total poster area = 200 in^2

Side margins = 1 inch each

Top and bottom margins = 2 inches each

Let x = length of the full poster

then 200/x = width of the full poster

Therefore, the length of the printed area = x - 3.5

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

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

Solving for the Area (A) of the printed space, we have

 

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

 

A = 700 -2x2

 

If the derivative is set to 0, we have:

0 = 700 -2x2

 

700 = 2x2

 

350 = x2

 

x = 18.70829  The original length

 

width = 10.69045

 

Therefore, the area of space available for printing is

 

15.20829  *  8.69045

 

= 132.1669 in^2