A poster is to have an area of 240 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. Width and height?
Let the dimensions of the poster are L and W.
==> Then the area of the poster is :
A = L*W = 240
Now the dimensions with margins are:
Bottom and top : (w-2)
sides : (L-3)
==> Now the area is:
But `L= 240/W`
`==gt A = (w-2)(240/w - 3) `
`==gt A = (24 - 3w - 480/w + 6) `
`==gt A= -3w - 480/w + 30`
Now we will find the maximum value.
`==gt A'= -3 + 480/w^2 = 0 `
`==gt 480/w^2 = 3 ==gt w^2 = 480/3 = 160 `
`==gt w = sqrt160 = 4sqrt10 `
`==gt L= 480/w = 480/(4sqrt10) = 120/sqrt10= 12sqrt10`
Then, the dimensions that gives the maximum area are:
`4sqrt10 ` and `12sqrt10` .