SOLUTION: Poster is to be designed with 50 in^2 of printed type, 4 inch margins on both the top and the bottom, and 2 inch margins on each side. Find the dimensions of the poster which minim

Algebra ->  Surface-area -> SOLUTION: Poster is to be designed with 50 in^2 of printed type, 4 inch margins on both the top and the bottom, and 2 inch margins on each side. Find the dimensions of the poster which minim      Log On


   

Question 1009763: Poster is to be designed with 50 in^2 of printed type, 4 inch margins on both the top and the bottom, and 2 inch margins on each side. Find the dimensions of the poster which minimize the amount of paper used
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the picture. x and y dimensions of the poster. x for horizontal, y for vertical.

A=xy for area function;
%28x-2%2A2%29%28y-2%2A4%29=50

Use the print-type region equation, .... y=50%2F%28x-4%29%2B8 and substituting into A, omitting to show the steps here,
highlight_green%28A%28x%29=%2850x%29%2F%28x-4%29%2B8x%29.

Taking derivative of that in preparation to find optimized values,
dA%2Fdx=%28%28x-4%2950-50x%2A1%29%2F%28x-4%29%5E2%2B8
and again omitting further algebra steps for the derivative,...
highlight_green%28dA%2Fdx=%288x%5E2-64x-72%29%2F%28x-4%29%5E2%29

Set that equal to 0, solve for x, and find corresponding y value.

Focus on the numerator to be set to 0.
8x%5E2-64x-72=0
x%5E2-8x-9=0
%28x-9%29%28x%2B1%29=0

The meaningful value for x is highlight%28x=9%29.

Use that to find y
y=50%2F%289-4%29%2B8
highlight%28y=18%29