0
votes
2answers
32 views

Line that passes between two vectors

I encountered the following in a text book I'm reading and I can't seem to understand why this is true (I'm translating this into English so excuse me if I'm not using the correct english terms): ...
0
votes
0answers
27 views

Suppose I have the tableau below for a maximization problem. For the tableau to be optimal what are values for c1, c2, and b?

Suppose I have the tableau below for a maximization problem. For the tableau to be optimal what are values for c1, c2, and b? z x1 x2 x3 x4 x5 x6 RHS 1 c1 c2 0 0 0 0 10 ...
0
votes
0answers
26 views

Proving equivalence between basic feasible solution and vertex

I stumbled upon this proof of the Bertimas book on Linear optimization and I don't see what the "key ingredient" is that makes it work. Baxic feasible solution $\implies$Vertex Let $x^*$ be a ...
0
votes
1answer
9 views

What if objective function $Z$ is also in the constraints?

What if objective function $Z$ is in the constraints? To construct the dual form for this problem? how do I approach to this problem? Maximize $\;\;\;\;\;\;\; z$ subject to $$\;\;\;z - ...
0
votes
1answer
146 views

Minimizing shipping cost under given constraints

I have a question that has been bugging me for about a day now. A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines and Plant II needs at ...
0
votes
1answer
350 views

Minimize LPP using graphical method [ operational research ]

Question: Minimize z = 2x + 6y Subject to 2x + y >= 2; 3x + 4y <= 12 x,y >=0 Is min z = 2 the right answer ? if not how do i solve this ?
1
vote
0answers
23 views

Highest (lowest) index of positive time-indexed variable

I have a simple problem involving a variable $x_{it}$ representing the amount of a resource allotted to a task $i$ in time $t$. The quantity of the (renewable) resource is constrained at a value $R$ ...
0
votes
1answer
79 views

How to enforce a constraint that a decision variable can only take 1 of $k$ integer values?

How would you enforce the constraint that $x$, a decision variable, can only take values -3, 7, or 19? I think I probably need to introduce a binary variable here but not sure where to start. Thanks. ...
0
votes
1answer
65 views

How to solve a linear program with OR constraints

I have $n$ people. I want assign them to $c$ jobs. A job may be not assigned at all or there must be a minimum and maximum number of people assigned to it. $n$ is about 4000 and $c$ is about 1000. ...
0
votes
0answers
59 views

Simply formulated but hard problem on system of linear equations

When does the below system has a solution? $$AX=B\\ X > 0$$, where $A$ is $n\times n$ symmetric positive definite matrix and $X$ is a $n\times 1 $ column vector. Note: (I'm trying to use Farka's ...
0
votes
0answers
35 views

Finding the dual of a linear program

I have an exam next week and I would like to make sure I am doing this problem correctly and I would also appreciate if somebody could explain to me the purpose of duality? What is the ultimate goal ...
1
vote
1answer
996 views

Linear Programming Inventory Problem

I'm still trying to get used to the nature of these problems and I'd appreciate some further explanation. ...
2
votes
1answer
796 views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
3
votes
2answers
794 views

Financial Linear Programming Problem

I'm very new at linear programming and I'm trying to figure out a way to approach this problem below: ...
1
vote
0answers
604 views

Graphically solving a Linear Programming Problem?

I was given the following linear programming problem and have been asked to find all optimal solutions graphically. I am quite new to the subject, so please forgive my naivety. ...
1
vote
1answer
57 views

Integral Polyhedra: Integer on each face

The general topic is unimodular matrices and integral polyhedra. I am really new to this field and I am studying for an exam in an advanced operations research course. In this case we are always ...
0
votes
1answer
107 views

Partial linear relaxation yields an integer solution

Consider a binary integer program \begin{align} \min \quad &\sum _{j \in J}f_j x_j +\sum _{i \in I} c_i y_i \notag \\ \mbox{s.t.} \quad &\sum _{j \in N_i} x_j \ge 1-y_i, \quad \forall i\in I ...
2
votes
1answer
299 views

How to solve this LP problem as a Dynamic Programming problem?

The standard form LP problem is $$\min -3x_1-7x_2-10x_3 \text{ s.t. }$$ $$x_3\leq 2$$ $$40x_3+40x_2+20x_1\leq 180$$ $$x_1,x_2,x_3\geq 0$$ My last lecture covered the Bellman equation ...
0
votes
1answer
1k views

Example about the Reduced cost in the Big-M method?

I want to gather examples about the reduced cost in different cases, now for the Big-M method. I hope this makes the methods more accesible. So How does the Big-M method work with the below? ...
1
vote
1answer
292 views

Meaning of the bar over $\bf{c}'$ in $\bf{\bar{c}}'=\bf c' -\bf c'_B \bf B^{-1} \bf A\geq \bf 0$?

I am trying to understand the page 87 Bertimas about Linear Programming. The author uses bolding and bars -- now I am starting to think that the bar means something else to vector, bolding apparently ...
1
vote
1answer
389 views

Reduced cost in the Phase II of the two-phase Simplex?

My lecture slides outline how the two-phase simplex works: this table shows the end result of the phase I for the standard-form problem and the auxliary table of the phase I here. I understood until ...
1
vote
1answer
674 views

Warehouse Location Problem as an integer progam instead of a mixed-integer program

Given a set of costumers $M = \{1, \dots , m \}$ and a set of of factories $N = \{1, \dots , n\}$ we have $c_{ij} \geq 0$ costs to deliver to costumer $i \in M$ from factory $j \in N$ $F_j \geq 0$ ...
2
votes
0answers
331 views

Reconstructing an optimal Simplex tableau from an optimal solution

I have here a bounded LP with infinite optimal solutions: ...
1
vote
1answer
754 views

A question about the operation research and simplex method

For the simplex method, we need to add slack variables. My question is how to determine how many slack variables should be considered in the LP problem? I don't quite get why in the cases to find out ...