A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $6 per foot and fencing for the other two sides costs $10 per foot. What is the maximum area that can be enclosed for $5400?

Question

anonymous · Answer

i think something is wrong it is not right

mathstudent55 · Answer

Let one dimension be called L
The other dimension is called W

The area of a rectangle is:
A = LW

The Perimeter, P = 2L + 2W
The cost of the fencing is:
6*2L + 10*2W = 5400
12L + 20W = 5400
20W = 5400 - 12L
W = 270 - 0.6L

Substitute the expression for W into the expression for the Area
A = L(270 - 0.6L)
A = 270L - 0.6L^2
Take the derivative
dA/dL = 270 - 1.2L

Set the derivative equal to zero, and solve for L
270 - 1.2L = 0
1.2L = 270
L = 225
Substitute to get W
W = 270 - 0.6(225) = 135

Length = 225 ft, Width = 135 ft
A = 225 ft * 135 ft = 30,375 sq ft

anonymous · Answer

thanks God bless u it is right now. have great night.