SOLUTION: The top and bottom margins of a rectangular poster are each 2 inches long, and the side margins are each 1/2 inch long. If the area of the printed material on the poster is fixed a

Question 982771: The top and bottom margins of a rectangular poster are each 2 inches long, and the side margins are each 1/2 inch long. If the area of the printed material on the poster is fixed at 64 square inches, find the dimensions of the poster with the smallest area A. Also draw a picture of the situation. Please give details on how this would be solved. Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The top and bottom margins of a rectangular poster are each 2 inches long,
and the side margins are each 1/2 inch long.
If the area of the printed material on the poster is fixed at 64 square inches,
find the dimensions of the poster with the smallest area A.
Also draw a picture of the situation.
:
Let L = the length of the printed material
Let w = the width of the printed material
We know L*W = 64
L =
:
The 2" top and bottom adds 4" to length
the 1/2 sides add 1" to width
therefore the area of the poster will be
A = (L+4)*(w+1)
FOIL
A = Lw + L + 4w + 4
We know Lw = 64, therefore
A = 64 + L + 4w + 4
A = L + 4w + 68
replace L with
A = + 4w + 68
:
plot this equation

minimum area occurs when w = 4" is the width of the text
then
64/4 = 16" is the length of the text
:
"find the dimensions of the poster with the smallest area A."
16+4 = 20" the length of the poster, (2" margin top and bottom)
and
4 + 1 = 5" the width of the poster, (1/2" margin on each side)
RELATED QUESTIONS
A 25-by-37-inch sheet of paper is to be used for a poster, with the shorter side at the... (answered by kitkat02)

A page of a certain book is 12 inches high and 8 inches wide. The top and bottom margins... (answered by KMST)

Any help solving this would be GREAT!! Bob is laying out the pages of a book. Each... (answered by stanbon)

A 26-by-31-inch sheet of paper is to be used for a poster, with the shorter side at the... (answered by josgarithmetic)

The top and bottom margins of a poster are each 6 cm and the side margins are each 4cm.... (answered by stanbon)

A 26-by-31-inch sheet of paper is to be used for a poster, with the shorter side at the... (answered by josmiceli)

The top and bottom margins of a poster are 6 cm and the side margins are each 6 cm. If... (answered by ikleyn)

Word Problems involving Optimization (Derivatives) A poster must have a printed area... (answered by mananth,ikleyn)

Word Problems involving Optimization (Derivatives) A poster must have a printed area... (answered by mananth,ikleyn,greenestamps)