Question

A rectangular box is to have a square base and a volume of 40 ft^3. If...

A rectangular box is to have a square base and a volume of 40 ft^3. If the material for the base costs $0.36/ft^2, the material for the sides costs $0.05/f^2, and the material for the top costs $0.14/ft^2, determine the dimensions of the box that can be constructed at minimum cost.

length____ft

width____ ft

height________ ft

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A rectangular box is to have a square base and a volume of 16 ft3. If...
A rectangular box is to have a square base and a volume of 16 ft3. If the material for the base costs $0.14/ft2, the material for the sides costs $0.06/ft2, and the material for the top costs $0.10/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.) A closed rectangular box has a length of x, a width of x, and a height of y.
A rectangular box is to have a square base and a volume of 20 ft3. If...
A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.37/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.13/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.
A rectangular box is to have a square base and a volume of 20 ft3. If...
A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.17/ft2, the material for the sides costs $0.06/ft2, and the material for the top costs $0.13/ft2, (a) determine the dimensions (in ft) of the box that can be constructed at minimum cost. (b) Which theorem did you use to find the answer?
Minimizing Packaging Costs A rectangular box is to have a square base and a volume of...
Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.28/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.22/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.) A closed rectangular box has a length of x, a width of x, and a height of y. x...
A rectangular box is to have a square base and a volume of 48 ft3. If...
A rectangular box is to have a square base and a volume of 48 ft3. If the material for the base costs 4 cents per square foot, material for the top costs 20 cents per square foot, and the material for the sides costs 16 cents per square foot, determine the dimensions of the square base (in feet) that minimize the total cost of materials used in constructing the rectangular box.
A rectangular box is to have a square base and a volume of 45 ft3. If...
A rectangular box is to have a square base and a volume of 45 ft3. If the material for the base costs 14 cents per square foot, material for the top costs 6 cents per square foot, and the material for the sides costs 6 cents per square foot, determine the dimensions of the square base (in feet) that minimize the total cost of materials used in constructing the rectangular box.
A rectangular box with a volume of 272 ft. cubed is to be constructed with a...
A rectangular box with a volume of 272 ft. cubed is to be constructed with a square base and top. The cost per square foot for the bottom is15cents, for the top is10cents, and for the other sides is 2.5 cents. What dimensions will minimize the​ cost? What are the dimensions of the box? The length of on side of the base is ___ The height of the box is___ (Rounds to one decimal place as needed)
A box with square base and open top is to have a volume of 10?3 ....
A box with square base and open top is to have a volume of 10?3 . Material for the base costs $10 per square meter and material for the sides costs $8 per square meter. Determine the dimensions of the cheapest such container. Use the first or second derivative test to verify that your answer is a minimum.
rectangular tank with a square​ base, an open​ top, and a volume of 8788 ft^3 is...
rectangular tank with a square​ base, an open​ top, and a volume of 8788 ft^3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
A company plans to manufacture a rectangular box with a square base, an open top, and...
A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 404 cm3. The cost of the material for the base is 0.5 cents per square centimeter, and the cost of the material for the sides is 0.1 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost?