A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 per foot, while the remaining two sides will use standard fencing costing $2 per foot. The budget that will be entirely used for fencing is $6000. In order to maximize the area of the plot, how many feet of standard fencing should be purchased for the project?

1700 ft

Step-by-step explanation:

Let the dimensions of the plot of land be x any y

Where:

Perimeter of the Land=2x+2y

Cost of Fencing =$3(2x)+$2(2y)=6x+4y

The budget that will be entirely used for fencing is $6000.

Area of the Land, A(x,y)=xy

Substitute into A(x,y)

The Area is maximized when its derivative equals zero.

3000-4y=0

4y=3000

y=750

Recall:

Therefore: x=500ft, y=750ft

Since side y is fenced using standard fencing,

Feet of standard Fencing required = 2y=2 X 750 =1500 ft