please please help Calculus problem?
a farmer wants to fence off land along a river into five equal areas by using one section of fence parallel to the river and six sections perpendicular to it. what should the dimensions be to maximize the total area using 1200 feet of fence? (assume that the river is straight and that no fence is required along the river
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Let y be the width(s) and x be the length of the rectangular fence.
Perimeter = x+6y = 1200
6y=1200-x
y=200-x/6
Area = xy = x(200-x/6) = 200x-x^2/6
Differentiate the area with respect to x
dA/dx = 200 - 2x/6 = 0
1200 = 2x
x=600 feet
y= 200-200/6 = 166.67 feet width
d^2A/dx^2 = -2 < 0, so the area has been maximized.