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

The total width of each row of the pens should be ???

the total height of each column of pens should be???

maximum area???

Answer 1

A= wh

650 = 6w + 2h

2h = 650-6w

A = w(650-6w)/2 = 325w -3w^2

A'(w) = 325 -6w = 0

w = 325/6 = 54 1/6 feet wide

h = 325/10= 32.5 feer high

max A = 650/12 x 325/10 = 1,760.40681 ft^2