Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
A farmer has 200 m of fencing to enclose a rectangular field bordered on one side by a river (no fence is needed along the river). Find the dimensions (width × length along the river) that maximize the enclosed area.
- 50 m x 100 m
- 40 m x 120 m
- 60 m x 80 m
- 100 m x 100 m
Answer
A. 50 m x 100 m
Solution
Let x = width (the two sides perpendicular to the river) and y = length along the river. Then 2x+y=200 y=200-2x. Area A=xy=200x-2x2. A'=200-4x=0 x=50, so y=100.
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