Maximum/minimum problem (max. printed area of sheet)

G

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Guest
A sheet of paper for a poster has an area of 6msquared. The margins at the top and bottom are 0.75m and at the sides are 0.5m. Show that the dimensions for a maximum printed area are 2m in length and 3 metres in width.
 
I see your post count is well over 100. You should have learned by now that failure to show ANY effort is not encouraged.

What's your plan?
Draw a picture?
 
this is my plan...

i have drawn the picture...

i know that x * y = 6

and that the total printed area will be

6 - (x-1)(y-3/2) = 6 - (x-1) (2y-3/2)

= 2y + 3x - 9 - 2xy all divided by 2...

I get stuck here...where do I go from here...
 
You're a little off.

The area of the poster is \(\displaystyle \L\\xy=6\)...[1]

The area of the print is \(\displaystyle (x-1)(y-1.5)=xy-1.5x-y+1.5\)...[2]

Solve [1] for y and sub into [2], differentiate, set to 0 and solve for x. y will follow.
 
Excellent response. Showing what you are doing is orders of magnitude more important than you might expect. Do that from now on - without making us ask. :D
 
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