Question

An open-top rectangular box is being constructed to hold a volume of 300 in3. The base...

An open-top rectangular box is being constructed to hold a volume of 300 in3. The base of the box is made from a material costing 8 cents/in2. The front of the box must be decorated, and will cost 12 cents/in2. The remainder of the sides will cost 2 cents/in2.

Find the dimensions that will minimize the cost of constructing this box.

Front width: _______ in.
Depth: ________ in.
Height: ________ in.

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 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?
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 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.
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...
ASAP A company plans to manufacture a rectangular container with a square base, an open top,...
ASAP A company plans to manufacture a rectangular container with a square base, an open top, and a volume of 320 cm3. The cost of the material for the base is 0.8 cents per square centimeter, and the cost of the material for the sides is 0.2 cents per square centimeter. Determine the dimensions of the container that will minimize the cost of manufacturing it. What is the minimum cost?
A pencil cup with a capacity of 48 in^3 is to be constructed in the shape...
A pencil cup with a capacity of 48 in^3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 40¢/in^2 and the material for the base costs 60¢/in.^2, what should the dimensions of the cup be to minimize the construction cost? A pencil cup is in the shape of a rectangular box with a square base and an open top. height ____ in length...
A rectangular storage container with an open top and a square base is to be constructed....
A rectangular storage container with an open top and a square base is to be constructed. Material for the bottom costs $6/sq-ft, and material for the sides costs $3/sq-ft. If a total of $72 is budgeted for material expenses, what are the dimensions of the container that holds the largest volume?
Minimizing Costs A pencil cup with a capacity of 45 in.^3 is to be constructed in...
Minimizing Costs A pencil cup with a capacity of 45 in.^3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 27¢/in.^2 and the material for the base costs 90¢/in.^2, what should the dimensions of the cup be to minimize the construction cost? A pencil cup is in the shape of a rectangular box with a square base and an open top. height length...
A box with a square base and open top must have a volume of 202612 cm3....
A box with a square base and open top must have a volume of 202612 cm3. We wish to find the dimensions of the box that minimize the amount of material used. (Round your answer to the nearest tenthousandths if necessary.) Length = Width = Height =
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT