# Tagged Questions

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

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### Which Denominations to use for payroll with no returned change

I want to solve the following problem. It is not a homework. Assume that a company pays payroll to employees every period, the sum of the salaries for period is $T$. The accountant goes to the bank ...
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### Linear Optimization proof. Duality proof.

I need help with this problem. The exact problem is in this link http://d2vlcm61l7u1fs.cloudfront.net/media%2F959%2F959d289e-6f26-4e21-875e-bb71f3f5a49f%2Fphprimn1q.png Sorry for the poor formatting. ...
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### (Revised Simplex Method) How is B-inverse computed in this Linear Optimization example?

I've been trying to figure this out for a while, so I'm hoping somebody might be able to shed a few insights. I've been looking through this example problem that uses the Revised Simplex Method: https:...
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### Is $f(x)=-3x_1+x_2-x_3^2$ pseudoconvex at $\bar x$?

Is $f(x)=-3x_1+x_2-x_3^2$ pseudoconvex at $\bar x=[-115/588, -95/588, 5/14]^T$? Pseudoconvexity: If $\nabla f(\bar x)^T(x-\bar x)\ge0$, then $f(x)\ge f(\bar x)$ for any $x\in \mathbb{R^3}$ (in this ...
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### Compute the singular value of matrix

I would like to prove that for a matrix $A$ with dimension $p \times q$, and dim$(A)=q$, define a p+q by p+q symmetric indefinite matrix B with zero diagonal blocks and with A and $A^T$ in the off-...
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### Unbounded variables and dual of a linear program

I have to find the dual of \begin{cases} \max & -x_1 &-2x_2+x_3\\ & -3x_1 &+x_2&\le-1\\ & x_1 &-x_2&\ge 1\\ & -2x_1 &+7x_2&\le6\\ & -5x_1 & +...
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### Finding a particular vector given a basis

I am trying to implement a code for Karmarkar's algorithm for solving linear programming problems. I want to automate the selection of the initial vector on the basis of the constraint vector $A$ ...
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### Linear integer programming

I am trying to find the optimal solution for the following linear integer programming: \begin{eqnarray} &&\underset{x_i, \forall i} {\text{maximize}} ~ \sum_{i=1}^N x_i a_i \\ && \...
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### How to find all basic feasible solutions of a linear system?

I'm trying to solve this problem but need some help getting started. The problem asks to find all the basic feasible solutions of the following system: $$-4x_2+x_3=6$$ \...
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### Find the dual of the lp problem

The problem given is and I need to find the dual: Min $Z=x_1$ st. $x_1+x_2 \leq 4$ $x_2 \geq 0$ So this is what I did, I said: Let $x_1=x_1'-x_1''$ where $x_1',x_1'' \geq 0$ So now ...
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### characteristic cone of polyhedral

Let $$Q=\{x ∶ Ax ≤ b \}≠∅$$ If $Q = P + C$, where $P$ is a polytope and $C$ is a polyhedral cone, prove that $$\{y|Ay ≤ 0\} = \{y|x + y ∈ Q, ∀ x ∈ Q\}$$ The cone $C = \{y|Ay ≤ 0\}$ is called ...
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### Is there a way to determine if the Convex Hull of two polyhedra is going to be huge?

So in this post: Faster Algorithms for Convex Hulls I was interested in determining if a convex hull of two $n$ dimensional polyhedra can be computed quickly, and the answer was in general: no, ...
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### Linear programming exercise verification

I am working on this exercise (translation mine): A Motel provides a 24 hour service and needs a minimum number of workers depending on the time slot: ...
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### What programs or websites solve linear integer or goal programming problems?

I don't think I can use Excel. My solver doesn't work so I can't even use Excel for regular linear programming. Something like this but for integer or goal programming. This seems to allow integer ...
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### Prove that optimal Solution exist without solving.

![1]: http://i.stack.imgur.com/Osa3G.jpg Without solving the problem, show that it has an optimal solution.
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