I am having trouble with 2 volume and a profit problems?

[rockstar14]

I need help solving these problems. My teacher gave me these as examples to practice on for an upcoming test and I am really in need of some help. So if anyone is willing to explain each one and work them out from start to finish. I would greatly appreciate it!

1. A rectangular box with a square base and open top is to be constructed to have a volume of 108m cubed. What are the dimensions of the box that will require the least amount of material?

2. An open rectangular box is to be made from a 24in. by 9in. rectangular piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the box with the largest volume that can be made?

3. A manufacturer determines that in order to sell x mp3 players, the price per player must be p=740-x. The total cost of producing x players is C(x)=5000+100x. How many players must the manufacturer produce in order to maximaze profit?

 

[arildno]

Steps for Problem 1:
1. Let "h" be the height of the box, "a" the side of the square.
Formulate, as an equation, what it means that the volume equals 108!

2. The amount of material is measured by the total surface area.
Set up the function, of "a" and "h" that measures the total surface area!

3. Utilize the result in 1. to eliminate one of your variables, in order to transform the result in 2. into a function of ONE variable.

4. try to minimize the value of THAT function, gained in 3.

 

[arildno]

As for Problem 2:
Call the side in the congruent sqeares "x".
What becomes the length, breadth and height for a box in that case, and what is the wolume function, in terms of "x"?

 

[Mark44]

rockstar14,
These appear to be homework problems, so they should be posted in the Homework & Coursework section, not here in the math technical section.

Please repost each problem in its own thread, and include the work you have done.

I am locking this thread.
Mark44