A fence is to be built to enclose a rectangular area of 240 square feet. The fen

Question

A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 12 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

Dimensions:________ x _____________

(1 pt)

Check the boxes of the points where the graph has an global maximum (ANSWER F)

A. 0
B. 1
C. 3
D. 5
E. 6
F. 7

Check the boxes of the points where the graph has an global minimum (asnwer C)

A. -0.7
B. 0
C. 1
D. 2
E. 4
F. 6
G. 7

Check the boxes of the points where the graph has a local maximum idk the answer

A. 0
B. 2
C. 3
D. 4
E. 5
F. 6
G. 7

Check the boxes of the points where the graph has a local minimum idk the answer

A. -0.7
B. 0
C. 1
D. 3
E. 4
F. 5
G. 6

Explanation / Answer

Solution:

A rectangle with area of 240 and sides of L and W

so L x W = 240
and L = 240 / W

For the cost analysis

L = $4/ft and W = $4/ft and $12/ft

So 2*L(ft) * $4/ft + 1 * W(ft) * $4/ft + 1*W(ft) * $12/ft = cost of the fence

substitute L = 240 / W

2*(240/W)*4 + 4W+12W = cost

1920/W + 16W = cost

To find the lost cost take the derivative of the left hand side and set it equal to zero and solve

=> -1920 / W^2 + 16 = 0
=> W^2 = 120 ft
=> W = 10.95 ft

Solve for L

L = 240 / W = 240 / 10.95 = 21.92 ft

So dimensions L X W = 21.92 X 10.95

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