Rectangular poster of area 6912 cm^2 side margins of 8 cm and top and bottom margins are 6 cm.

Question

Find the dimensions of the  poster that gives the maximum printing area?

 

How will I start with this? How will I know the domain? what will be my constraints? aside from the formula for area, should I also use the formula for the perimeter? thanks!

Answer 1

?????????? "find  dimenshuns" ??????...yu wanna no how big????

???????? printing area ????????? yu wanna maximize area inside the borders????

1. rektangel with area=6912 , so leng*wide=6912, or wide=6912/leng

2. top & bottom border=6

3. side border=8

inside area=(leng-16)*(wide -12)

=(leng-16)*[(6912/leng)-12]

=6912 +(12*16)-12*leng -(16*6912)/leng

=6912 +192 -12*leng -110592/leng

d(area)/dx=-12  -110592*(-1)*leng^-2

max area wen slope=0, so -12 +110592*leng-2=0

or -12 leng^2 +110592=0

or leng^2=110,592/12=9216

leng=root(9216)=96

wide=area/leng=6912/96=72