Question

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

Answer 1

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)

`C = 36 L + (8* 480)/(L)`

Differentiate with respect to L

`(dC)/(dL)=36 - (3840)/(L^(2))`

Put it equal to zero.

L² = 106.67

L = 10.33 feet

So, W = 46.48 feet