# Tagged Questions

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

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### Knight movement on chess field

I had this task in programming competition: There are two knights, which are $(p_1,q_1)$ and $(p_2, q_2)$. $(p,q)$ knight is figure, with p(q)-length first step, and q(p)-length second step in ...
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### Simplex/Big-M/Dual Simplex methods

I just want to know when to use which method. This is my current understanding, please say if I am incorrect: If all constraint equations can be turned into s.t. the RHSs of all are positive and all ...
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### Interpretation or definition of “shadow prices”

I do understand that shadow price associated to a resource is the marginal profit you would get if you buy one more unit of that resource. I also know that it is the minimum profit you would accept to ...
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### How to formulate constraints given the following information

The following question was given in one of my class but none of us got the use of the market requirements in the problem: A form produces and sells three products namely Product1, Product2 and ...
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### Limmiting solution of $Ax=b$ to positive quantities

My personal trainer put me on a diet recently which has had me tracking the macro-nutrients that I eat i.e. protein, carbohydrates and fat. I am supposed to eat a specific amount each meal and eat ...
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### Linear programming: Condition on index variable

Let $i \in \{1,2,...n\}$. And let $X_i \in \{0,1\}$. I need to write the condition: if all $X_i$ where $i$ is even index take the value 1, then there need to be at least three $X_i$ with value $0$ ...
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### Linear Programming with target values.

I'm trying to figure out the general solution to a min-max problem. The general form of the problem is as follows: ...
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### Which optimization class does the following problem falls into (LP, MIP, CP..) and which solver to use

I have the following optimization problem. I want to solve it using a computer solver. But I am not sure which problem class it falls into or which solver to use. Problem: There is a set of objects ...
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### Solution of the LP relaxation - always round to the nearest integer?

If an optimal solution to the LP relaxation of an IP is not integer, can we always get a feasible IP solution by rounding it to the nearest integer? Or can we generalize this process by saying, if we ...
The primal problem is as followed: Minimize $z=4x-5y$ Subject to $y\le10-x$, $y\le2+3x$, $x,y\ge0$ Write out its dual and solve it geometrically. ...I have found its dual and graphed out the ...