Question

A closed three dimensional box is to be constructed in such a way that its volume...

A closed three dimensional box is to be constructed in such a way that its volume is 4500 cm cubed. It is also specified that the length of the base is 3 times the width of the base. Find the dimensions of the box that satisfies these conditions and has the minimum possible surface area.

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 closed rectangular box is to be constructed with a base that is twice as long...
A closed rectangular box is to be constructed with a base that is twice as long as it is wide. If the total surface area must be 27 square feet, find the dimensions that will maximize the volume.
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 closed rectangular box is going to be built in such a way that its volume...
A closed rectangular box is going to be built in such a way that its volume corresponds to 6m3. The cost of the material for the top and bottom is $ 20 per square meter. The cost for the sides is $ 10 per square meter. What are the dimensions of the box that produce a minimum cost?
A box with an open top has a square base and four sides of equal height....
A box with an open top has a square base and four sides of equal height. The volume of the box is 225 ft cubed. The height is 4 ft greater than both the length and the width. If the surface area is 205 ft squared. what are the dimensions of the​ box? What is the width of the box?. What is the length of the box?
A box with a square base and closed top must have a total surface area of...
A box with a square base and closed top must have a total surface area of 600 cm2. Find the dimensions of the box that maximize its volume (clearly identify the decision variables, the constraints, and the objective function. You have to prove that the dimensions you get in the end are truly the dimensions for the maximum volume, and not the minimum or anything else)
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...
A 10 ft3 capacity rectangular box with open top is to be constructed so that the...
A 10 ft3 capacity rectangular box with open top is to be constructed so that the length of the base of the box will be twice as long as its width. The material for the bottom of the box costs 20 cents per square foot and the material for the sides of the box costs 10 cents per square foot. Find the dimensions of the least expensive box that can be constructed.
A manufacturer sends you 100m2 of material to construct a box (single layer, closed top). The...
A manufacturer sends you 100m2 of material to construct a box (single layer, closed top). The box must have a square base and be of maximum volume. Let sbe side length the base of the box, and hthe height of the box. a) Write an equation for the surface area covered by the material. b) Determine a formula for the volume V as a function of the side of s only. c) Determine the dimensions such that of the box...
A box with a square base and open top must have a volume of 108000 cm^3....
A box with a square base and open top must have a volume of 108000 cm^3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT