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

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0votes1answer18views

if else statement linear programming

I am trying to work out an if else statement for the following problem, which should be mathematically linear programmed: when both item 1 and item 2 are picked, both their costs are reduced with 20%. ... user avatar Milouw

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2votes1answer26views

Assignment Problem (Hungarian): Does increasing a match-specific payoff always make it more likely to be selected?

I'm thinking about the assignment problem for assigning $I$ workers to $I$ tasks (let $I=J$ so there are the same number). Suppose that each possible assignment yields a payoff of $u_{ij}$. I want to ... user avatar ABC

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0votes0answers11views

Prove that a standard form primal LP has a nondegenerate optimum if the corresponding dual form LP's optimal is unique & nondegenerate

This is Exercise 4.13 from Bertsimas' Introduction to Linear Optimization. The original question asks that the standard form primal optimum is unique and nondegenerate iff the dual is unique and ... user avatar Yash Kumar

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-5votes0answers35views

Linear programming by simplex method [closed]

Solve by using simplex method of $\max z=40x_1+88x_2$ Subject to $2x_1+8x_2\leq 60$ $5x_2+2x_2\leq 60$ $x_1,x_2>0$ user avatar Sybil

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0votes0answers25views

How else can I solve how much decaf and caffeinated coffee should go in my brew?

I want 39mg of caffeine in my 20oz of coffee. blend1 has 9mg / 8oz. blend2 has 91mg / 8oz. it takes me 26g of coffee to produce 20oz. assuming blend1 and blend2 weigh the same, how many grams of ... user avatar R. Tero

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0votes1answer22views

My linear program has multiple optimal solutions. I want that corner point at which the value of one of the variables is the maximum?

Is there a way to find the optimal point with this special property in polynomial time? Note that the polytope in the linear program may be unbounded. user avatar Zing

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1vote1answer27views

How do you determine the best solution out of a set of feasible basic solutions/extreme points?

I'm working on one of my exam sets, surrounding linear optimization, and could really use some help. The assignment is essentially $\to$ find the $10$ basic solutions $\to$ find the $5$ feasible ... user avatar Thybo

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-1votes0answers16views

When does dual simplex algorithm terminate? [closed]

I'm trying to get my head around the dual simplex method. I want to know about the cases where the algorithm terminates. I would like to know what condition must be met to tell if: Prime feasibility ... user avatar user1984131

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0votes0answers11views

Parametric linear program with parameterization only in the objective

I am working with a parametric linear program of the following kind where the parameter c is changing: \begin{array}[t]{l} \min c^{\top} x\\ s.t.\\ \quad A x \ge b\\ \quad 0 \le x \le x^{u} \end{array}... user avatar Zing

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1vote1answer26views

How to prove that solution have at most $m$ fractional coordinates

I started to study a bit of mixed linear programming, and I am facing the following exercise that after quite some time I don't know how to approach: Let $A\in\mathbb{R}^{m,n}$, $b\in\mathbb{R}^{m}$, ... user avatar P-Adic-Gatito

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1vote0answers35views

A minimax optimization with $\ell_p$ constraint

I have a minimax with general $\ell_p$ constraint optimization problem. The objective function is in the following, $$\min_{\mathbf{w} \in \mathbb{R}^d} \mathbb{E}_{(\mathbf{x}, y) \sim P}[\max_{\... user avatar Andy Meow

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Matrix optimization - sum of largest element in each column

Feel free to tweek particular expressions if it will make it easier to find a solution. In the end, I will end up with an approximate anyway: $V$ is a given $N\text{ x }m$ complex matrix with columns $... user avatar Gappy Hilmore

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Finding all integer solutions for a Linear Program over the Birkhoff Polytope

I have the situation where the Birkhoff Polytope is the space of all valid solutions to a linear function I am interested in maximizing. It is my understanding that, because the vertices of the ... user avatar Michael Keller

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2votes1answer41views

How to apply matrices to dnd style games

While playing a game, I needed to match 5 Characters to 5 Classes to optimise my team. I've listed the classes each character is suited for: Mage-2,4 Ninja-1,2 Thief-3,5 Warrior-1,2,4 Cleric-2,3,5. I'... user avatar Robin Ting

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1vote1answer43views

How to linearize z <-> x == y?

I have a constraint that reads $z \iff x = y$ where $z$ is a 0-1 variable and $x,y$ are non-zero, positive integer variables. I'm managed to formulate equivalence going in the right direction, but not ... user avatar gablin

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