A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $12 per foot and on the other three sides by a metal fence costing $4 per foot. If the area of the garden is 200 ft, find the dimensions of the garden minimizing the cost. (Let x be the length of the brick wall and y be the length of an adjacent side in feet.)

The dimensions of the garden that will minimize the costs are: x=10ft, y=20ft

Step-by-step explanation:

Let x be the length of the brick wall. Let y be the length of the adjacent sides.

Area of the garden = 200 ft

Therefore: xy=200

Perimeter of the Fence = Length of

brick wall+Length of Opposite Metal Fence + Length of Other Adjacent Metal Fence

=x + x + 2y

Costing of brick wall= $12 per foot Cost of Metal =$4 per foot.

Cost of the Fence=12x+4x+4(2y)

=16x+8y

Recall:

Therefore, the cost in terms of x is:

The minimum costs C(x) occur when its derivative equals zero.

Thus:

x=10ft

Recall that:

y=200/10=20 ft

The dimensions of the garden that will minimize the costs are: x=10ft, y=20ft

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step-by-step explanation:

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step-by-step explanation:

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