A canvas 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.

Answer: The depth of the shelter for which the space inside is maximized is 3.5 ft.