MAT 110-IL1 Summer 2017 Test: Test 3 Time Remaining: 01.18.08 Submit Test This Q

Question

MAT 110-IL1 Summer 2017 Test: Test 3 Time Remaining: 01.18.08 Submit Test This Question: 1 pt 210121 (0 complete) This Test: 25 pts possible Farmer Ed has 150 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? The width, labeled x in the figure, is Type an integer or decimal.) meters The length, labeled 150-2x in the figure, is meters (Type an integer or decimal.) The largest area that can be enclosed is [] square meters. (Type an integer or decimal) Enter your answer in each of the answer boxes. tion P.4Conce

Explanation / Answer

Answer: Width, x = 37.5 mtrs; Length, 150 - 2x = 75 mtrs; Largest area = 2812.5 sr/mtrs. (As shown below)

The area that can be enclosed = x (150 - 2x) = 150x - 2x2

dA/dx = 150x - 2x2 = 0 for max or min and we get:

150 - 4x = 0.

So, x = 150 / 4 = 37.5.

Again differentiating 150x - 4x second time, we get the second derivative for 150x - 2x2 as -4, which is less than 0.

Therefore, it is local maxima.

So, maximum width is 37.5 mtrs and length is 150 - 2x = 150 - 2(37.5) = 150 - 75 = 75 mtrs.

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