Question

A rectangular garden of area 300 square feet is to be surrounded on three sides by a brick wall costing $ 10 per foot and on one side by a fence costing $ 5 per foot. Find the dimensions of the garden such that the cost of the materials is minimized.

Answer 1

Answer:

15 and 20 feet

Explanation:

The computation of the cost of the material minimized is shown below:

As we know that

Area of rectangle = Length × Width

where,

Length be X

Width be Y

So, the equation is

X × Y = 300 square feet

X = 300 ÷ Y

Now the another equation is

C = 10 × (Y + Y + X) + 5X

C = 20Y + 15X

So we can write

C = 20Y + 15 ×  300 ÷ Y

C = 20Y + 4,500 ÷ Y

Now apply the derivatives

So,

DC ÷ DY = 20 - 4,500 ÷ Y^2 = 0

20Y^2 = 4,500

Y = 15

So X = 20

The C = Cost