A poster is to have an area of 180 in^2…?
with 1 in margins on the sides and bottom and a 2 in margin on the top. What dimensions will give the largest printed area?
PLEASE SHOW WORK THANK YOU!!!!
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Let w = width (in inches)
then 180/w = height (in inches)
So the printed width would be w – 2
and the printed height would be 180/w – 3
Then the printed area is
f(w) = (w – 2)(180/w – 3)
f(w) = 180 – 3w – 160/w + 6
f'(w) = -3 + 160/(w^2)
0 = -3 + 160/(w^2)
3 = 160/(w^2)
3w^2 = 160
w^2 = 160/3
w = sqrt(160/3)
w = 4/3 * sqrt(30)
I’ll let you find the height. I hope this helps!
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