Question
A farmer with 3000 feet of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?
Answers
Area = A x B
Total length = 3000 = A + 2B
B = (3000-A)/2 so,
Area = A x (3000-A)/2 =
= 3000A/2 - (1/2)A^2
take 1st derivative
0 = 1500 - A and solve for A
A = 1500 and B = 750
Total length = 3000 = A + 2B
B = (3000-A)/2 so,
Area = A x (3000-A)/2 =
= 3000A/2 - (1/2)A^2
take 1st derivative
0 = 1500 - A and solve for A
A = 1500 and B = 750
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