Aposter is to have an area of 210 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. find the exact dimensions that will give the largest printed area.

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210 = (h+3) (L +2) = h L + 3 L + 2 h + 6 
or 
h L + 3 L + 2 h = 204 
L(h+3) = 204-2h 
L = (204-2h)/(h+3) 

A = L h 
A = h(204-2h)/(h+3) 

for max dA/dh = 0 
= h[(h+3)(-2) -204+2h]/(h+3)^2 +(204-2h)/(h+3) 

=h[-2h-6-204+2h]/(h+3)^2 +(204-2h)/(h+3) 

=-210 h/(h+3)^2 + (204-h)(h+3)/(h+3)^2 
= zero for max 
so numerator = 0 
0 = -210 h + 204 h -h^2 +612-3h 

0 = -h^2 -9 h + 612 

h^2 + 9 h - 612 = 0 

h = [ -9 +/- sqrt (81+2448) ]/2 

h = [ -9 +/- 50.3 ]/2 

h = 20.64 
L = (204-2h)/(h+3) 
= 6.89 

1. 3/6 or 1/22. 1/123. 1/84. 1/105. 2/12 or 1/6