maxima question. The question is weirdly worded. In essence, I need to determine the dimensions and maximum volume of a rectangular prism(bag) if the sum of the length, width and height can't exceed 156.

Question

anonymous · Answer

A maximized rectangular prism is a cube.  Therefore, you can simply divide 156 by 3... 156/3 = 52.

52*52*52 = Max volume

52+52+52 = 156.

anonymous · Answer

Thanks for quick reply. Sorry but can I ask why it has to be a cube? I will need to justify my answer for assignment paper.

anonymous · Answer

The next part of school question goes on and asks what the result would be if max depth was 24 cm? or the width were half of length? I assume there must be a formula.

anonymous · Answer

You can prove it many ways, I prefer calculus, but truthfully you can probably get an explanation just googling it.  "Maximized rectangular prism is a cube".

Now you can do 156 - 24 (for the depth)
156-24= 132

Divide 132 by 2 (2 remaining items - length and width) 66.

Therefore L=66, W=66, D=24

66*66*24 = Max volume

66+66+24 =156

anonymous · Answer

I will leave the last one up to you, you should be able to figure it out.

anonymous · Answer

Thanks. Very helpful. Can I ask one more question: What is the best software solution to graph equations (without doing programming or paying a fortune) that look textbook like? Been stuck for ages on this.

anonymous · Answer

It depends, do you go to a university? You can usually download Mathematica for students free of charge. If not, then you can use WolframAlpha (website). For example: http://www.wolframalpha.com/input/?i=x^2%2By^2%3D9 You can get 3D graphs as well, that is just an example.

anonymous · Answer

Thank you