# Questions tagged [linear-programming]

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

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### Theta-Ratio of a Simplex Method for a degenerate solution, are they always equal?

Are the $\theta$-ratios of two degenerate solutions always equal? So as to say: If we know two unique points yield the same objective value, must their $\theta$-ratios always be equal? For two ...
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### Special Case of the Two Phase-Method

I'm sorry this question must be slightly vague. In the two-phase method, my general understanding is that you try to exit your Aritifical Variables to make your Auxillary problem to $0$. But what ...
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### Linearize nonlinear equality [closed]

Is there any way to linearize following equality for using Lp solvers in an optimization problem? $x-x^2=0$
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### Linear Programming Price Change After X Units Sold

I have a question regarding writing some formulas for LP. How would you code the price change after X number of units sold. So lest say the base price for the first X units sold is £5 and then there ...
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### Constraints of a linear programming problem

QUESTION Sandy Arledge is the program scheduling manager for WCBN‐TV. Sandy would like to plan the schedule of television shows for next Wednesday evening. Of the nine possible one‐half hour ...
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### Need help defining a Quadratic Programming problem

I have an optimization problem which should be solvable with Quadratic Programming: There are $n$ multiplication coefficients $c_i$ for which optimized values are searched. The coefficients are ...
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### How to find the $K$-nearest neighbor vertexs in a polyhedron defined by a set of linear inequalities?

Consider a polyhedron $\mathcal{P}$ defined by a set of linear inequalities, i.e., $$\mathcal{P} = \left\{ x \in \{0,1\}^N \mid Ax\le b \right\}$$ Suppose $\mathcal{P}\neq \emptyset$. If I have a ...
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### Cycling in Simplex Method - Smallest Subscript Rule

Could someone explain to me how using the smallest subscript rule causes a cycling LP to terminate? At the moment it looks to me that a program would use it to determine whether the matrix from the ...