Answer:

Step-by-step 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=
 
        
             
        
        
        
Answer: Brand B is 
Explanation 
(Brand A)24 diapers is 0.29¢ per diaper
(Brand B) 50 diapers is 0.27¢ per diaper
        
             
        
        
        
8x.......................