Maximize the printable region of a poster.

Problem statement:

A poster of P square inches is to be constructed with top and bottom
margins t inches and left and right margins r inches. Determine the
dimensions of the poster so that the "printable" region has maximum area.

Note: Some Examples to use:

#1. 3" by 5" card = 15 sq. in. 
For a card with 15 sq. in and 1/4" margins all around
what is the optimal size to maximize the printable area?

#2. 8.5" by 11" sheet of paper = 93.5 sq. in.
For a sheet with 93.5 sq. in with top & bottom 1" margins 
and left and right 1.25" margins what is the optimal size 
to maximize the printable area? (Note some word processors 
uses these margins as default values.)

#3. 8.5" by 14" legal sheet of paper = 119 sq. in.
For a sheet with 119 sq. in with top & bottom 1" margins 
and left and right 1.25" margins what is the optimal size 
to maximize the printable area? 

#4. 14" by 22" poster board = 308 sq. in.
For a board with 308 sq. in with top & bottom 2" margins 
and left and right 3" margins what is the optimal size 
to maximize the printable area? 

#5. 20 by 30" mounting board = 600 sq. in.
For a board with 600 sq. in with top & bottom 3" margins 
and left and right 3" margins what is the optimal size 
to maximize the printable area? 

#6. 12.375" by 21.75" sheet of newsprint = 269 sq. in. (approximately)
For a board with 269 sq. in with top & bottom 2" margins 
and left and right 1" margins what is the optimal size 
to maximize the printable area? 

The accompanying animation uses Area = 500 sq.in., top and bottom margins 3 in.,                                                        and left and right margins 5 in.