Select an objective function for which this model has no optimal solution. Then work through the simplex method step by step to demonstrate that Z is unbounded.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Q1 Suppose that the following constraints have been provided for a linear programming model with decision variables x1and x2

- x1,3x2< 30

-3x1+ x2<30

and

x1>0 x2.0

I) Demonstrate graphically that the feasible region ¡s unbounded.

ii) If the objective is to maximize Z - x1+ x2, does the model have an optimal solution? If so, find ¡t. If not, explain why not.

iii) Repeat part (ii) when the objective is to maximize Z = x1- x2.

iv) For objective functions where this model has no optimal solution, does this mean that there are no good solutions according to the model? Explain. What probably went wrong when formulating the model?

v) Select an objective function for which this model has no optimal solution. Then work through the simplex method step by step to demonstrate that Z is unbounded.

Q2 hydroelectric power systems planning

An agency controls the operation of a system Consisting of two water reservoirs with one hydroeJec power generation plant attached to each as Shown in  Fig. 2.1. The planning horizon for the system is broken into two periods. When the reservoir is at full capacity, additional inflowing water is spilled over a spillway. In addition, water can also be released through a spillway as desired for flood protection purposes. Spilled water does not produce any electricitý.

Q3:

i) Reformulate this problem to fit the canonical form for a linear programming model.

ii) Using the Big M method, work through the simplex method step by step to solve the problem.

iii) Using the two-phase method, work through the simplex method step by step to solve the problem.

iv) Compare the sequence of 8F solutions obtained ¡n parts (b) and (c). What conclusion you can derive from this comparison?

Attachments:

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme