# calc 3

posted by .

A cardboard box without a top is to have volume 500000 cubic cm. Find the dimensions which minimize the amount of material used. List them in ascending order.

• calc 3 -

A.
You can assume symmetry between length and width, which reduces to the width(=length) and the height.
Furthermore, one of the two can be eliminated from the volume relation:
w^2h=500000
So the minimization problem is reduced to one single dimension as in elementary calculus.

B.
The same results can be obtained by calculating the area of material required:
A=2h(b+w)+bw + L(bwh-500000)
the second term introduces the Lagrange multiplier.
Take partial derivatives with respect to w,b,h and L and solve for each variable from the 4 equations.
This method should give the same results as in part A.

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Calculus

1. Chris makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square to the nearest hundredth of …
2. ### calculus

A box with a square base and an open top is to have a volume of 68in^3 . Neglect the thickness of the material used to make the box, and find the dimensions of the box that would minimize the amount of material used. The width and …
3. ### Pre-calc

A cardboard box with an open top and a square bottom is to have a volume of 45 ft3 . Use a table utility to determine the dimensions of the box to the nearest 0.1 foot that will minimize the amount of cardboard used to construct the …
4. ### josh

A cardboard box without a top is to have volume 500000 cubic cm. Find the dimensions which minimize the amount of material used. List them in ascending order.
5. ### calculus

An open rectangular box having a volume of 256 is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x by …
6. ### Calculus

An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize the …
7. ### Calculus

A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used.
8. ### Calc

A box with a square base and no top is to be built with a volume of 4000 in3. Find the dimensions of the box that requires the least amount of material. How much material is required at the minimum?
9. ### Calculus 1-Optimization

A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used. sides of base cm height cm
10. ### Math (calc)

An open box with a square base is to have a volume of 12ft^3. Find the box dimensions that minimize the amount of material used. (round to two decimal places). it asks for the side length and the height. Please help asap due in a few …

More Similar Questions