Optimisation with 3 variables Help. (designing food containers)

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Lukaide

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Hey so i have an assignment where i need to come up with 2 designs for canned food containers. These designs must be made of two basic shapes combined and have a volume of 600cm. There also has to be 3 UNRELATED variables. So basically i need to create the shapes like a cylinder with a cone on top and then find the minimum surface area using optimisation in order to minimise the cost. my issue is that from my knowledge you need 1 variable to do this, and i can get one variable in terms of the other by using volume formula but then im still stuck with 2 different variables. Please help :)
 
Update: i figured out 1 shape, cylinder with cone on top. now just one more.
 
You can still have 3 variables (one diameter and 2 heights), and use constrained (by volume) optimization. Or you can use a truncated cone and reduced 4 constrained variables (one diameter and 3 heights) to 3 unconstrained ones.
 
blamocur said:
You can still have 3 variables (one diameter and 2 heights), and use constrained (by volume) optimization. Or you can use a truncated cone and reduced 4 constrained variables (one diameter and 3 heights) to 3 unconstrained ones.
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Can you elaborate on how you would solve using the first method (1 diameter and 2 heights)
 
thekezzad said:
Can you elaborate on how you would solve using the first method (1 diameter and 2 heights)
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Can you elaborate on your question? I.e., do you agree about 3 variables? Can you express the constraint in terms of those variables? How about the objective function?
 
blamocur said:
Can you elaborate on your question? I.e., do you agree about 3 variables? Can you express the constraint in terms of those variables? How about the objective function?
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Yes I agree about the 3 variables. It would be the volume of the cylinder and cone equal to 600 and the objective function would be the surface area
 
Lukaide said:
cylinder
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thekezzad said:
How did you figure out this one? I’m interested to know.
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turns out its not exactly right. my 3 variables were height radius and slant height. but the teacher said slant height isnt allowed as a variable as its not independent. its found by the height and radius. He also said the height of cone and cylinder arent allowed to be the same which is annoying. so what i have to do is actually do the shape with 4 variables, get it down to 2 then literally go through HEAPS of numbers and find the value that gives the most minimum. so an approximation which is annoying
 
Lukaide said:
turns out its not exactly right. my 3 variables were height radius and slant height. but the teacher said slant height isnt allowed as a variable as its not independent. its found by the height and radius. He also said the height of cone and cylinder arent allowed to be the same which is annoying. so what i have to do is actually do the shape with 4 variables, get it down to 2 then literally go through HEAPS of numbers and find the value that gives the most minimum. so an approximation which is annoying
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So you’re pretty much picking different values for the radius and one of the heights until it gives you the lowest surface area?
 
Lukaide said:
my 3 variables were height radius and slant height. but the teacher said slant height isnt allowed as a variable as its not independent.
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I'd argue that those 3 variables are inter-dependent (thanks Pythogoras), but choosing slant height is less convenient because it has to be larger than the straight height and larger than the radius. Straight height and the radius have no limitations.

Do you have the exact text of the assignment, or is your post a transcription of verbal instructions?
 
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