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linear programming problem

QUE 1

Consider the following .

The tableau corresponds with a step of the SIMPLEX method applied to the previous problem.

  1. What is the value of the variables  and the objective function?
  • Identify the entering and the leaving variables. Justify your response with the calculations performed (you can extend the previous tableau to perform the required calculations)
Entering Variable:   Leaving Variable:
  • Based on the information summarized in the sensitivity report of Excel (corresponding to the optimal solution, answer the following questions.
  1. How it affected the value of objective function if the right side of the third constraint increase in 2 units? Justify with the calculations performed
  • How many units is possible to increase the right side of the third constraint without losing the geometry of the current optimal solution

Que 2.

The ABC Company is planning to replace its current electrical infrastructure with a new special system. Since the new system has more capacity it is not necessary to maintain all the current connections. The manager wishes to decide which pairs of offices should be directly connected in order to ensure that every office is connected (directly or indirectly) in the new system. The figure shows the current infrastructure: the letters represent the offices and the arcs, the connections. The numbers represent the distances between the corresponding nodes.

 In order to minimize the cost: What are the offices that must be directly connected? Assuming that for the new system is required 3 units of cable for each unit of distance, how many units of cable should be purchased by the company? Justify with the calculations performed.

  1. Is this problem P or NP? Justify

Que 3.

The town hall of a city wants to open some recreational centers. It has been analyzed 3 options. The opening cost and the capacity of each center are listed below.

The selected recreational centers must be hosting the students from 5 schools. In the table below is summarized the number of students at each school.

Each school must be assigned to only one recreational center. And the capacity of each center must be respected. What are the recreational centers that must be open in order to minimize the opening cost?

  1. Formulated a mathematical programming model. (Linear Model is required)
  2. Modify the previous model such that are considered the following constraints:
  3. One school can be assigned to several recreation centers
  4. It is decided to open at most two recreation-center
  5. Design a greedy solution strategy for the problem described in 1.
  6. Illustrate the greedy procedure with the following data:

Que 4.

Answer the following questions:

  1. What is a flow-oriented simulation software (such as FlexSim) used for? 
  2. Explain why simulation software’s are used?

Answer the following questions related to FlexSim software:

  • The main resources found in any simulation model are source, queue, processor and sink. Briefly explain the role of each.
  • Which kind of connection may be used to connect the above-mentioned resources?
  • What does the “machine throughput” measure?

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