You want to build a rectangular box in such a way that the sum of the...

You want to build a rectangular box in such a way that the sum of the length, width and height is 24 cm.
a) Define the equations so that the dimensions of their volume are maximum
b) Which of the equations proposed would be the restriction and which function? Explain
c) Using the technique you want to calculate maximums and minimums, what are these values? What volume will the box have?

Expert Solution

milcah answered 2 years ago

Mandeep’s parents want to build a rectangular ice rink in the family’s back yard with an...

Mandeep’s parents want to build a rectangular ice rink in the family’s back yard with an area of 200m2 What are the dimensions that will minimize the amount of material required to build the boards around the rink? If the material for the boards can be bought for $1.75 a linear foot, how much will it cost to build the boards? Trevor was given 15 square concrete stones with a 1 ft. side length. He decides to make a slab...

You are making a box by removing the corners from an 16cm by 10cm rectangular box....

You are making a box by removing the corners from an 16cm by 10cm rectangular box. How much do you need to remove to make a box of maximum value? Please show explanation

We want to design a rectangular box without a lid with a volume of 64000 cm^3....

We want to design a rectangular box without a lid with a volume of 64000 cm^3. Find the dimensions that maximize the surface area. Using Lagrange Multipliers Can you explain your reasoning pls

An open-top rectangular box has a volume of 250 cm 3. The width of the box...

An open-top rectangular box has a volume of 250 cm 3. The width of the box is 5 cm. The cost is $2/ cm 2 for the base and $1/ cm 2 for the other sides. What is the minimum cost for making the box?

A box with an open top is to be constructed out of a rectangular piece of...

A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=10 ft and width=11 ft by cutting a square piece out of each corner and turning the sides up. Determine the length x of each side of the square that should be cut which would maximize the volume of the box.

A cereal box, in the shape of a rectangular prism and with a closed top, is...

A cereal box, in the shape of a rectangular prism and with a closed top, is to be constructed so that the base is twice as long as it is wide. Its volume is to be 8000cm3。 Find the dimensions that will minimize the amount of cardboard required to make the box.

A rectangular box with no top is to be made to hold a volume of 32...

A rectangular box with no top is to be made to hold a volume of 32 cubic inches. Which of following is the least amount of material used in its construction? a.) 80 in2 b.) 48 in2 c.) 64 in2 d.) 96 in2

If you needed to reduce deflection in a loaded aluminum rectangular box beam in your structural...

If you needed to reduce deflection in a loaded aluminum rectangular box beam in your structural design, which of the following variables would you INCREASE? : -Length -Outer width -Outer height -Inner width -Inner height Which would be the MOST effective in reducing deflection? What material could you substitute for aluminum in your design to decrease deflection? Why?

A rectangular box is to have a square base and a volume of 40 ft3. If...

A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.35 per square foot, the material for the sides costs $0.05 per square foot, and the material for the top costs $0.15 per square foot, determine the dimensions of the box that can be constructed at minimum cost. = Length Width Height how do i find length width and height

As a farmer, suppose you want to fence off a rectangular field that borders a river....

As a farmer, suppose you want to fence off a rectangular field that borders a river. You wish to find out the dimensions of the field that occupies the largest area, if you have 1200 feet of fencing. Remember that a square maximizes area, so use a square in your work. Draw several diagrams to express the situation and calculate the area for each configuration, then estimate the dimension of largest possible field. Find the function that models the area...

Question