Question 162778: As a real estate tycoon you have bought a rectangular parcel of waterfront property and want to enclose your land as follows: Using 5000 feet of fencing you want to enclose a rectangular section on only three sides using the water as the 4th side. What dimensions (length and width of the rectangle) should the enclosure be to assure maximum area?
I have been working on this problem for over two hours, it's ripping my mind apart! PLEASE HELP.
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! THE MAXIMUM AREA FOR A FENCE AROUND 3 SIDES OF A RECTANGLE IS:
1*1*2=4 EQUAL MEASUREMENTS.
5,000/4=1250 FT.
SO YOU'LL HAVE 2 SIDES=1,250 EACH & 1 SIDE=2*1,250 OR 2,500 FT.
1,250+1,250+2,500=5,000 FT. OF FENCING.
1,250*2,500=3,125,000 FT^2 IS THE MAXIMUM AREA ENCLOSED.
PROOF:
REDUCE EAACH OF THE TWO 1,250 FT. FENCES BY 1 FOOT & INCREASE THE 2,500 FT FENCE BY 2 FT.
1,249*2,502=3,124,998 FT^2.
OR DECREASE THE 2,500 FT FENCE BY 1 FT & INCREASE EACH OF THE 1,250 FT FENCES BY 0.5 FT.
2,499*1,250.5=3,124,999 FT^2.
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