Answer:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
Step-by-step explanation:
Let the dimensions of the box be x, y and z
The rectangular box has a square base.
Therefore, Volume of the box
Volume of the box
The material for the base costs , the material for the sides costs
, and the material for the top costs
.
Area of the base
Cost of the Base
Area of the sides
Cost of the sides=
Area of the Top
Cost of the Base
Total Cost,
Substituting
To minimize C(x), we solve for the derivative and obtain its critical point
Recall:
Therefore, the dimensions that minimizes the cost of the box are:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet