A farmer builds a rectangular grid of pens with 1 row and 5 columns using 650 feet of fencing. What dimensions will maximize the total area of the pen?

Question

Width of each row of the pens ???

Height of each column of the pen??

Answer 1

Let x be the width of each column of the row and y be the height.

+---+---+---+---+---+

| | | | | | y

+---+---+---+---+---+

x x x x x

Total fence:

10x + 6y = 650

y = (650-10x)/6

Area, A= 5xy

A(x) = (5/6)x(650-10x) = (5/6)(650x-10x²)

A'(x) = (5/6)(650-20x)

Set to zero and solve for x

x = 65/2 = 32.5 feet

y = (650-325)/6 = 325/6 ≈ 54.167 feet

Total width of the row = 5(32.5) = 162.5 feet