4 votes
Accepted

Minimizing distance of the mean from a point

As in my answer to the linked question, let binary decision variable $y_i$ indicate whether $x_i \in A$. You want to minimize $$\left|\frac{\sum\limits_{x_i \in X} x_i y_i}{\sum\limits_{x_i \in X} ...
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3 votes
Accepted

How often should I invest considering that each additional investment has a transaction fee?

It seems clear that you should invest periodically, because whatever is the right time to wait for the first investment after you make it you are starting in the same place except you have this ...
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2 votes

Best possible way to withdraw amount from different accounts

You can solve this as a generalized maximum flow problem with semicontinuous flows. Let $a_i$ be the initial amount in account $i$, and let $M=\sum_i a_i$. Let continuous decision variable $t_{ij} \...
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2 votes
Accepted

Finding the greatest sum of 10 integers with a given set of constraints.

You can solve the problem via integer linear programming as follows. Let binary decision variable $x_{sc}$ indicate whether space $s$ contains counter $c$. Let $u_c$ be the upper bound on the number ...
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2 votes

Relationship Between a "Minimum Spanning Tree" and a "Tour"?

The idea for a proof that the MST cost is at most the TSP cost is in the screenshot you provided. Take an optimal TSP tour with cost $z_\text{TSP}$ and remove one edge, yielding a spanning tree with ...
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1 vote

How often should I invest considering that each additional investment has a transaction fee?

There is an analytical solution to the problem Starting from @Ross Millikan's answer, writing $$(100k-25)\frac {i^n-1}{i^k-1}=(100(k-1)-25)\frac {i^n-1}{i^{k-1}-1}$$ simplifying, we end with $$\frac{(...
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1 vote

nonlinear optimisation problem

You can solve the problem via integer linear programming as follows. Let binary decision variable $x_i$ indicate whether entry $i$ is selected. The problem is to maximize $\sum_i A_i x_i$ subject to ...
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1 vote

Finding the greatest sum of 10 integers with a given set of constraints.

Since you have $(11)$ counters total, and $(10)$ spaces, the best that you can do is to use $(10)$ of the counters, if possible. So, you have two simultaneous goals to strive for: Maximize the ...
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1 vote

Given n objects shared by several sets of known sizes, what is the minimum number of objects shared by all the sets?

A general approach is to use integer linear programming, with a nonnegative decision variable $x_S$ for each of the nonempty subsets $S$ of the given sets and linear constraints to enforce the ...
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