Acanvas wind shelter like the one at right is to be built for use along parts of the guadalupe river. it is to have a back, two square sides, and a top. if 147/2 square feet of canvas is to be used in the
construction, find the depth of the shelter for which the space inside is maximized assuming all the canvas is used.

A = 2 a² + 2 a b 
2 a² + 2 a b = 147/2
a² + a b = 36.75
a b = 36.75 - a²
b = ( 36.75 - a² ) / a
V = a² * b
V = a² * ( 36.75 - a² ) / a
V = 36.75 a - a³  ( maximum of the volume is when V` = 0 )
V` = 36.75 - 3 a²
36.75 - 3 a² = 0
3 a² = 36.75
a² = 36.75 : 3
a² = 12.25
a =√12.25
a = 3.5 ft
b = 24.5 / 3.5 = 7 ft.
The depth of the shelter for which the space inside is maximized is 3.5 ft.