farmer builds a rectangular grid of pens with 1 row and 6 columns using 950 feet of fencing. What dimensions will maximize the total area of the pen?

Question

 farmer builds a rectangular grid of pens with 1 row and 6 columns using 950  feet of fencing. What dimensions will maximize the total area of the pen? 

The total width of each row of the pens should be 

the total height of each column of pens should be 

which gives the maximum area of 

Answer 1

Draw and label a diagram!

c represents the length of a column

475 - 3c represents the length of the row

A(c) = c(475 - 3c)

A(c) = 475c - 3c²

Maximum is at c = -475/(2)(-3) or c = 79 1/6 ft.