Optimization: Maximize the Volume of Closed Box | (Ali BA)

To solve optimization problems:
1- Determine what the problems asks us to find.
2- Sketch and label the problem. This is helpful to visualize the problem.
3- Drive a function from what is given & determine the Interval. You need to write this function in term of one variable, so you need another equation to write the other variable in term of the first one.
4- Find global max or min based on what the problem is asking.

Remember:
Volume of a box = length * width * height
Area of rectangle is = length * width
Area of square is = (length)^2

Note, dimension are always positive (length and volume is positive)

To write the volume in term of 1 variable, you use the surface area to solve for h. Then, substitute h value in the volume function.

To find global max:
1)Find critical points
2)Evaluate critical points and endpoints in the function
3)Determine global max. The highest value is where is the global max.

If you have any questions or suggestions, let me know in the comments below.

Table of content:
00:00 Part a
06:06 Part b
08:00 Part c