Answer:

Explanation:
Let
Side of square base=x
Height of rectangular box=y
Area of square base=Area of top=

Area of one side face=

Cost of bottom=$9 per square ft
Cost of top=$5 square ft
Cost of sides=$4 per square ft
Total cost=$204
Volume of rectangular box=

Total cost=




Substitute the values of y

Differentiate w.r.t x







It takes positive because side length cannot be negative.
Again differentiate w.r. t x

Substitute the value

Hence, the volume of box is maximum at x=2.2 ft
Substitute the value of x

Greatest volume of box=
