Question

A poster of total area 256 in2 is to have a margin of 4 inches at the top and bottom and 1 inch at each side.
(a) Find the dimensions of the poster which give the largest printed area.
I got: 32 height in; 8 width in
But I'm having trouble with this part.

(b) Suppose that, instead, we know the poster will contain 256 in2 of printed material with margins of 4 inches at the top and bottom and 1 inch at each side. Find the dimensions of the poster that minimize its total size.
height in
width in

Answer 1

But I got the first part right, so should I treat each margin as it's own thing like i did in the other one?

Answer 2

you know that (A) is correct with your answers?

If so, I may not have the correct approach.

Answer 3

Yes I got green check marks lol. It's an online math hw site

Answer 4

thanks!

Answer 5

@byerskm2 For part B, try it like this...

Let the height and width of the printed part be h and w. So h * w = 256 sq in.

Then, the outside area of the whole poster is A = (h+8)(w+2)

Then substitute in using h = 256/w from the first equation. This will allow you to get an equation of function for the outside area all in the variable w... A(w), in other words.

Then find dA(w)/dw, and solve for w that makes the derivative equal 0. Then go back and solve for h.