Optimization question?

Question

A poster is to contain 120 square cm of printed matter, with margins of 5.5 cm each top and bottom and 1.5 on each of the sides. Find the minimal cost of the poster if it is to be made of material costing 18 cents per square cm.
The minimal cost in dollars is_______???

Answer 1

I'll give you a clue...

First you make 2 of your own equation:

1st equation: (x+2(5.5))(y+2(1.5)) = 120

See if you can get it from here

Answer 2

120 = w*h

We want to minimize the margins, which are:

m = 2(w*5.5) + 2(h*1.5) + 4(1.5*5.5)
m = 11w + 3h + 33

h = 120/w

m = 11w + 3(120/w) + 33
m = 11w + 360/w + 33
m' = 11 - 360/w^2
w^2 = 360/11
w = sqrt(360/11)
w = 5.72 cm
h = 120/5.72 = 20.98 cm

So the total width = 5.72 + 2(1.5) = 8.72cm
total height = 20.98 + 2(5.5) = 31.98cm

area = (8.72)(31.98) = 278.87 cm^2

Cost = 278.87 * 0.18 = $50.20

Hope this helps!