Optimization with 1 equation with 3 variables

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Chemical Engineer here so my programming is not that good. I am wondering if there is a way to find the minimum of a variable, 'x'. There is only one equation, and I'd like to find the minumum of 'x' by optimizing 'y' and 'z.' I know that I could plug in numbers, but is there a way for Matlab to automatically do this for me? Thank you!
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Victoria
Victoria on 13 Apr 2019
So there is no way for me to get a lw that is not -infinty? Would it be better to bound it? I'm trying to get minimal lost work, and D2 and P1 are diameter and pressure respectively. If not, I will just result to do it by hand. Both P1 and D2 will not be zero
Walter Roberson
Walter Roberson on 13 Apr 2019
Review your equation. R1 is linear in P1, so minimum would be when P1 is minimum. R1 is inversely proportional to D2, so the minimum would be when D2 is maximum. Together with your bounds, that already tells you D2 = 10 and P1 = 0 . And then your equation is linear in lw, so you can make the result infinitely negative by making lw infinitely negative.
If the goal were to permit lw to be negative but that the overall minima of the function has to be >= 0, then provided you are willing to approximate 0.149 as 149/1000 instead of the actual [0.1485, 0.1495) range that 0.149 actually represents, then there is an exact solution that works out as approximately -137.34 . If you impose a lower bound of 0 for lw, then the minimum of the function is when lw is 0, and the minima would be approximately 137.34, which would decrease if you permitted D2 to become larger.

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