You have three sheets of 2 × 4 m cardboard. You cut squares of side x...

You have three sheets of 2 × 4 m cardboard. You cut squares of side x from each of the twelve corners. You fold up the resulting flaps on the three sheets to make 3 open-topped boxes, and you use the twelve squares to form two cubes. Maximize the total volume

Expert Solution

To maximize total volume of a number of open topped boxes and cubic boxes made from card board of known dimensions

milcah answered 3 years ago

a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 ft.

a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Suppose that in part (a) the original piece of cardboard is a square with sides of length s. Find the volume of the largest box that...

From a thin piece of cardboard 4 in. by 4 in., square corners are cut out...

From a thin piece of cardboard 4 in. by 4 in., square corners are cut out so that the sides can be folded up to make an open box. What dimensions will yield a box of maximum volume? What is the maximum volume?

From a rectangular sheet measuring 250?? by 150??, equal squares of side ? are cut from...

From a rectangular sheet measuring 250?? by 150??, equal squares of side ? are cut from each of the four corners. The remaining flaps are then folded upwards to form an open box Find the value of x that gives the maximum volume and give your answer to 2 decimal places. Xmax= Calculate the volume to the nearest ??3. Vmax=

a. Squares with sides of length x are cut out of each corner of a rectangular...

a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 5 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Suppose that in part (a) the original piece of cardboard is a square with sides of length s. Find the volume of the largest box that...

2. Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard...

2. Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 6 in. wide, find the dimensions (in inches) of the box that will yield the maximum volume. (Round your answers to two decimal places if necessary.) smallest value=? in ?in largest value =?in 3. Minimizing Packaging Costs A rectangular box is to have a...

Two parallel thin sheets are placed 2 cm apart. The sheets are squares of sides 5...

Two parallel thin sheets are placed 2 cm apart. The sheets are squares of sides 5 m. Temperature of both sheets are constant with one at ?! = 15 °? and the other at ?! = -120 °?. The emissivity of surfaces can be assumed to be 1. Determine the rate of heat transfer between the plates assuming the gap between the plates is: a. Vacuum b. Filled with air at atmospheric pressure (air is not moving) c. Please state...

if 760 wbc are counted in 8 large squares (4 on each side) of a hemocytometer...

if 760 wbc are counted in 8 large squares (4 on each side) of a hemocytometer and the dilution is 1:10. what is the WBC count per uL

A cardboard cutting company received three orders to cut rolls to the measurements shown below: Order...

A cardboard cutting company received three orders to cut rolls to the measurements shown below: Order Width (meters) Length (meters) A 0.50 1000 B 0.70 3000 C 0.90 2000 This company buys the cardboard to be cut into two standard widths: 1 and 2 meters and then cuts it according to what each order requires. The standard rolls do not have a defined length, since for practical purposes the cardboard can be glued to comply with the required length. Formulate...

Write a MATLAB code for discrete least squares trigonometric polynomial S3(x), using m = 4 for...

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You throw a 20.0 g dart horizontally into the side of a small cardboard box of...

You throw a 20.0 g dart horizontally into the side of a small cardboard box of mass 45.0 g that is initially at rest on a tabletop. The coefficient of the kinetic friction between the cardboard box and the tabletop is 0.35. The dart remains stuck in the box, which slides 0.530 m on the tabletop before stopping. How fast did you throw the dart?

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