find the total width, height, and maximum area of the rectangular grid

Question

A farmer builds a rectangular grid of pens with 1 row and 9 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= ? feet,
the total height of each column of pens should be=? feet,
which gives the maximum area of= ? square feet.

Answer 1

Draw a diagram.

 

w = width of each column

l = length of the row

 

18w + 10l = 950             

10l = 950 - 18w

l = 95 - 1.8w

 

A = 9w(95 - 1.8w)

A = 855w - 16.2w²

 

maximum at w = -855 / -32.4

w ≈ 26.3888889

 

l ≈ 95 - 1.8(26.3888889)

l ≈ 47.5

 

Check:

18(26.4) + 10(47.5)

47.52 + 475

950.2

 

With the length and the width you can determine the total area.