Question

A poster is to have an area of 210in^2 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.

Answer 1

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
check arithmetic