# Questions tagged [simplex-method]

Questions that relates to the "simplex algorithm", from the mathematical optimization field

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### Determine basic feasible solutions in LP

Consider a linear programming problem \begin{align*} \min_x \; &c^Tx\\ \text{s.t. } & Ax \leq b. \end{align*} Assuming the constraints form a polyhedron, is there any way we can group the ...
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### Find at least one solution of system of equations with constraints

Consider the system of equations with constraints $$\begin{cases} x+y+z+t+u+v=3(a+b), \\ x+y+2(z+t)+3u=6b\\ 0 \leq x,y,z,t,u,v \leq 1, \end{cases}$$ here $0 \leq a,b \leq 1$ are fixed parameters....
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### Simplex algorithm and extreme points

For this question my short-hand is LP = linear program, BFS = basic feasible solution, SEF = standard equality form. Since the Simplex algorithm iterates from extreme point to extreme point (...
### Why has the objective function changed from $M=x+y$ to $-M = -16 + 4x + 4y - S_3 - S_4$?
I am studying optimisation and have come across an example of a maximisation problem: maximise $$M=x+y$$ subject to $$x+3y \leq 32 \\ 2x+y \leq 24 \\x+3y \geq 6 \\ 3x+y \geq 10 \\ x,y \geq 0$$ ...