Word Problems

[ajorden]

I am having difficulty with this problem.

In a 3rd world country there is a disaster. Though food is provided by some humanitarian orginizations, containers are needed to hold food. We need to make lunch boxes for the people.
1- draw a rectangle and label the lenght 8 1/2 inches and the width 11 inches. Put a square at each corner and lable each side of the square x.
2-Draw the lunch box in 3 dimension
3- Find the volumc of the open box, v(x) when the side of each squar is x inches long.
4- find v(x) when
x=1 inch
x=1 1/2 inch
x=2 inches
x=3 inches
5- State the length of the side x that will give the maximum volume based on the previous question.
6- State the area function, A(x) of the bottom of the box in terms of x.
7- State the x and y-coordinates of the vertex of the area function A(x) from the previous question.
8- Does the vertex give the maximum or minimum when we graph A(x).
9- Does this vertex help you design the lunch box that will hold the most food?

 

[ajorden]

Word Problem

I don't need help with questions 1 and 2. I have already drawn the picture of the box and labeled it.

 

[galactus]

For part 3, look at your picture with the squares cut out.

After you fold up the sides, how wide is the box?. How long is it?. How deep is it?.

Remember, volume of the box is LWH

Isn't the depth the same as the size of the cut out squares?.

If the width is 8.5 and you cut out a square on each side of width x, how wide is it now?.

Same idea for the length.

Come back and let me know what you arrived at for the volume.

After the volume is found the optimal size of the squares, x, will give the max volume.

 

[ajorden]

Word Problem

So for question 3 I have (8.5-2x)(11-2x). Is that right? Then for question 4 I put
8.5-2(1) X 11-2(1)=58.5
8.5-2(1 1/2) X 11-2(1 1/2)=44
8.5-2(2) X 11-2(2)=31.5
8.5-2(3) X 11-2(3)=12.5


Am I on the right page?

 

[ajorden]

Word Problem

Yes, I understand that V=LWH, and so I have 8.5*11, I just don't see where I am supposed to get the height.