# Tagged Questions

For questions on the $n$-simplex, an $n$-dimensional polytope with $n+1$ points.

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### Using the simplex method to find the minimum cost

A local food bank puts together complementary gift packages for its donors during their pledge drives. The bank's costs for each package are $\$4$dollars for the Bronze level package,$\$7$ dollars ...
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### Simplex Method -why does Gauss Elimination produce a new better solution?

In the simplex method, a tableau is created. An entering variable is generated and then using a criteria the exiting variable is also selected. This gives a pivot column and row and pivot element. The ...
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### What are the lawful operations in the simplex method?

Having the following: \begin{equation*} \begin{cases} \max& 3 x_1 & + 2x_2 & +4x_3\\ &x_1 &+ x_2 &+ 2 x_3 &\le 4\\ &2x_1 & &+3 ...
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### Number of 0-simplices after second barycentric subdivision of a standard simplex [closed]

What is the number of 0-simplices of a standard $n$-simplex after its second barycentric subdivision? By the way of counting, this number is 1, 5 and 25 for 0-, 1- and 2-simplices, respectively. ...
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### Barycentric subdivisions and labeling of $(d-1)$-simplex

I am trying to prove that it is always possible to label the vertices of the $k$-th barycentric subdivision of a $(d −1)$-dimensional simplex with labels $1, 2, . . . , d$ such that each simplex ...
If I have a linear programming problem e.g. $$\max 2x_1 + x_2$$ with these constraints $$x_1-2x_2 \leq 14$$ $$2x_1-x_2\leq 10$$ $$x_1-x_2 \leq 3$$ And I want to solve the problem starting from a ...