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R has many powerful libraries to handle operations research. This exercise tries to demonstrate a few basic functionality of R while dealing with linear programming.
Linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
The lpsolve package in R provides a set of functions to create models from scratch or use some prebuilt ones like the assignment and transportation problems.
Answers to the exercises are available here. If you obtained a different (correct) answer than those
listed on the solutions page, please feel free to post your answer as a comment on that page.
Please install and load the package lpsolve and igraph before starting the exercise.

Answers to the exercises are available here.

Exercise 1
Load packages lpSolve and igraph. Then, take a look at lp.assign to see how it works.

Exercise 2
Create a matrix representing the cost related to assign 4 tasks(rows) to 4 workers(cols) by generating integer random numbers between 50 and 100, with replacement. In order to make this exercise reproducible, define seed as 1234.

Exercise 3
Who should be assign to each task to obtain all the work done at minimal cost?

Exercise 4
Based on the resource allocation plan, how much we will spend to get all this work done?

Exercise 5
Take a look at lp.transport to see how it works. Set up the cost matrix by generating integer random numbers between 0 and 1000, without replacement. Consider that will be 8 factories(rows) serving 5 warehouses(cols).

Exercise 6
Set up the offer constraint by generating integer random numbers between 50 and 300, without replacement.

Exercise 7
Set up the demand constraint by generating integer random numbers between 100 and 500, without replacement.

Exercise 8
Find out which factory will not use all its capacity at the optimal cost solution.

Exercise 9
What is the cost associated to the optimal distribution?

Exercise 10
Create adjacency matrix using your solution in order to create a graph using igraph package.