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a refcfatqngular garden of area 480 square feet is to be surrounded on three sides by a brick wall costing 12$ per foot and on one side by a fence costing 8$ per foot. Find the dimensions of the garden such that the cost of the materials is minimized

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Answer:

Step-by-step explanation:

Area of rectangular garden, A = 480 ft²

Let the length is L and the width is W.

costing of three side brick is $ 12 per foot

cost of one side fence = $ 8

A = L x W = 480 .... (1)

Total cost, C = 3 L x 12 + W x 8

C = 36 L + 8 W

From equation (1)

[tex]C = 36 L + \frac{8\times 480}{L}[/tex]

Differentiate with respect to L

[tex]\frac{dC}{dL}=36 - \frac{3840}{L^{2}}[/tex]

Put it equal to zero.

L² = 106.67

L = 10.33 feet

So, W = 46.48 feet