# Tagged Questions

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

61 views

16 views

### Optimizing a set of rules to better predict the outcome of events

I'm trying to better predict the top three finishers of the next 1000 800m mens freestyle swimming race. I've got a set of rules to rate the swimmers: 1) Add 5 points if the swimmer won his last ...
173 views

### Prove an artificial variable that leaves the basis will never return.

This is in the context of the Big M Method in the simplex algorithm in linear programming. Prove an artificial variable that leaves the basis will never return. I have no idea how to start this. ...
866 views

120 views

127 views

### How does the Simplex method of solving LPs use the starting solution?

Say one looks at the LP (in slack form) and sees that assigning $0$s to all the non-basic variables doesn't give a valid solution but some other non-trivial assignment of values to the non-basic ...
31 views

### Formulating Solution for Branch and Bound

I have a linear programming question which I am setting up for a branch and bound solution. I am having issues with where to begin. The question is asking to find the minimum operating cost to ...
96 views

### Combining the duality principle and the graphical method

I am trying to minimize this linear program by combining the duality principle and the graphical method: I can't seem to find an example of how to approach this, can anyone show me how I would go ...
46 views

### How to find a polynomial of order $4$ which minimizes a given condition

How to find a polynomial $P(x)$ of order $4$ such that $\max\{\vert\ln(n)-P(n)\vert : 1\leq n \leq12\}$ is as small as possible? I guessed the solution with linear programming, but I don't know how ...
24 views

### Expressing nonlinear problem as LP

I am using GLPK to solve a simple linear problem. Given is a set of distances $d_{ij}$ between nodes of a graph. We want to assign to each edge a velocity $v_{ij}$ such that the average time of ...
43 views

### unnecessary constraint in optimization problem

I have some optimization problem (optimizing parameter $\alpha$)with those constraints: $$\alpha_i\ge0$$ $$\sum\limits_i \alpha_i y_i =0$$ and a third constraints: w-\sum\limits_i \alpha_i y_i x_i = ...
41 views

### Effective convexity criterion for the finite point set in $\mathbb{R}^3$

I need to find effective convexity criterion for the finite point set. Below there is description of what is meant by "effective" criterion. Definition. Let $M = \{A_{1}, \ldots, A_{n}\}$ be the ...
37 views

### Expressing a Set Using Linear Inequalities

Let $D = {x ∈ R^3: |2x1 − x2 + 3x3 + 1| + |x2 + 2x3 − 2| + |5x2 − 3x3| ≤ 10}$. Express D as the feasible solution set of a linear system of inequalities (meaning, a system of the form $Ax ≤ b$). How ...
413 views

### On the Proof of Fundamental Theorem of Linear Programming.

Having read the link: Why maximum/minimum of linear programming occurs at a vertex? I understand why the optimal solution of any linear programming problem must be on the corner or lies on a face of ...
46 views

### Take two pieces of wood one 84 inches the other 74 inches. Need to cut equal amounts of 12.5 inches and 7.75 inches. How to solve?

So the system would look something like this. 74" < 12.5x + 7.75y < 84" 60" < 12.5w + 7.75z < 74" y + z = x + w where x, y, w, z are natural numbers ...
55 views

### Non linear programming

Could you please help me in solving the problem posted below. A company uses a raw material to produce two types of products. When processed, each unit of raw material yields 2 units of product 1 and ...
49 views

199 views

### How to solve systems of linear equations of multiple variables (more than 3 to 100s)?

This was a question asked during an interview for programming job. And the bottom line was to write an alogrithm to solve such equations. As much as it numbed my neurons - it really provoked me. I had ...
A linear program is said to be in canonical form if it has the following format: Maximize $c^Tx$ subject to $Ax ≤ b$, $x ≥ 0$ where $c$ and $x$ are n-dimensional real vectors, $A$ is an $m × n$ matrix ...
I have put this into the form $0.5x_1 + 0.25x_2 + x_3=6$ $-x_1 - 3x_2 + x_4=-2$ $x_1 + x_2 = 10$ Is this correct? If so, how do I find a basic solution so that I can begin the simplex algorithm?