# Tagged Questions

Questions on linear programming, the optimization of a linear function subject to linear constraints.

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### Formulating an optimisation problem into a mixed-integer problem

I'm not sure if I understand this question and was wondering if anyone could provide any insight to an answer. The only thing I can think of adding is a constraint: "x2 = integer", so I'm clearly ...
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### How to linearize a double sum of product of binary variables?

I have a double summation of the form $$x_{kn}\sum_{k'\in K}\sum_{n'\in N} x_{k'n'} A_{k'n}\leq B_{kn},\quad\forall\; k\in K,n\in N$$ where $x_{kn}$ is a binary variable. How to linearize this ...
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### When modeling a multi-objective problem, is there a simple way of choosing to fully minimize one function, then to go on and minimize the second?

I am modelling a problem where I have two objectives. My goal is to fully minimize the first objective function, then choose among the solutions that fully minimized the first objective function to ...
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### Ray between vertex and point inside a polytope

Let $P$ be a polytope, let $v \in P$ be a vertex of $P$, and let $x \in P$ such that $x$ is not a vertex. Consider the ray $$\forall t>0, \phi(t)=v+t(x-v).$$ Let $t_0$ be the maximal $t$ such that ...
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### Conditions for uniqueness of solution to a linear system of equation

Consider a $n\times n$ M-Matrix $\mathbf{A}$ and a $n\times n$ non-negative and non-zero matrix $\mathbf{B}$. Also, let $\mathbf{x}$ and $\mathbf{b}$ be two (non-zero) n-column vectors. I am looking ...
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### Maximize system of linear equations

Suppose you have the system $$\begin{bmatrix} 4 & 3\\ 1 & 7\\ 5 & 9\\ 2 & 4\\ \end{bmatrix} \begin{bmatrix} x\\y\end{bmatrix}=\begin{bmatrix}b_1\\b_2\\b_3\\b_4\end{bmatrix}$$ How ...
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### Trying to sell the most batches of animals using linear programming

I'm trying to sell the most batches of animals... Let's say I have 200 dogs, 100 cats, and 100 ferrets. ...
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### AMPL - Step by Step mode

Is there a way to solve a problem using AMPL in a step by step(or a verbose, or a debug) mode? Preferably showing all basis exchanges? The manuals of AMPL make reference to script development, but i ...
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### Why can/should we use 5 instead of 10?

Problem: A pharmacy has a uniform annual demand for 200 bottles of a certain antibiotic. It costs \$10 per year for a storage place for one bottle, and$40 to place an order. How many times during ...
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### Enlarging a rectangle around its origin, to fit a containing rectangle, but the rectangle must be moved

EDIT: The math was easy/as expected. The bug was in a programming error related to HTML/CSS. Sorry everyone, thank you. I am coding a mobile UI where there is a view of a small card. When clicked, ...