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1

Your question is little broad and has two aspect: Theory and Application. If you are interested in scientific approach and academic literature this kind of thing is called Mathematical_optimization which is branch of Multi-objective optimization which is again a branch of Operations_research. In terms of mathematics of solving these problems multivariate ...

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Yes, a Monte Carlo simulation (MC) is what you need. It is a well known and documented approach with many uses in finance, science and engineering. MC simulations are used to simulate the returns of complex financial assets or in your case returns of business ventures under uncertainty. Your input variables ($x_1, x_2,\cdots, x_n$) are uncertain. If you ...

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I would try a Gradient Descent algorithm if possible, although this might take a little VBA knowledge. In general, finding the absolute minimum of a multidimensional problem like that is complicated and time consuming, but the gradient descent will find a local minimum easily. What you will need to do for worst case scenarios: Construct a cost function ...

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