# Questions tagged [linear-programming]

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

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### Non-Empty Random Set Construction

I am aware any set $$\mathbb{S} = \{x\in\mathbb{R}^n | A x \leq b\}$$ where $A\in\mathbb{R}^{q\times n}$, $q\in \mathbb{R}^q$ is convex, yet there is no guarantee it's also non-empty. Is there ...
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### Sensitivity on A Farmer's Case

I have questions, from Bazaraa's book (Linear Programming). I have calculated point a. This is the optimal table. Where $x_1$ is wheat, $x_2$ is corn, dan $x_3$ is soybeans. My question is, what ...
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### Linear programming problem and Newtonian mechanics

I am trying to learn Linear Programming. However, I don’t know how to solve the following problem. Maybe you can help, because I am curious to the right approach and solution for this problem. It ...
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### linear multivariate constant (known) jacobian optimisation problem with non linear constraints

apologies if I don't give all the information needed I'm a bit out of my depth here. I have a multivariate optimisation (I think) problem: y = f(x) Where x and y are both vectors of the same ...
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### Linear programming solution

How to prove a linear program that is feasible and bounded is maximised at one of the basic feasible solution?
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### Use $x\ge 0 \implies y = 1$ and $x<0 \implies y = 0$ into a linear programming solver

For a binary variable $y$ and another decision variable $x$, $x$ being integer, I want to be able to use the following two non-linear constraints into a linear solver: \begin{align} x\ge 0 \...
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### What is the proof for boundedness of the following LP problem?

\begin{array}{ll} \text{maximize} & Ax + By \\ \text{subject to}& Cz + Dw = 1 \\ & A’x + B’y \le C’z + D’w \\ &x, y, z, w \ge 0. \end{array} where A, B, C, D, A’, B’, C’, D’ are ...
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### What is the meaning of $k$ in this paragraph from “The Application of Linear Programming to Team Decision Problems” by Radner?

The attached paragraph is from "The Application of Linear Programming to Team Decision Problems." I do not understand how the profit depends on the capital limit $k$ (whose definition is also ...
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### Linear programming using MATLAB

I'm currently trying to solve a problem. According to some people I know it's a linear programming problem, however, I've not had the course just yet. Situation: At my warehouse we get different ...
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### Rewrite linear optimisation problem in canonical form

Preliminary notation: Consider a finite set $\mathcal{Y}\equiv \{1,...,L\}$ and a function $u:\mathcal{Y}\rightarrow \mathbb{R}$. Let $\Delta(\mathcal{Y})$ be the set of probability distributions over ...
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### How to add multiple cuts as lazy constraints

I have a minimization problem where I implement Benders decomposition and add my cuts as lazy constraints. I am able to add multiple cuts at each iteration since the sub problem is seperable. Also, I ...