Egeo412

Spring 2007

Assignment 3: Linear Programming Graphical Solution Assignment

Introduction:  Based on the simple two variable problem provided by my old advisor, Dr. Samuel Ratick of Clark University, and described below graphically solve this Linear Programming problem. To accomplish this task perform the indicated following steps.

 

Mike Leavitt the Administrator of the Environmental Protection Agency (EPA) has a decision problem that he has asked our class to analyze for the Agency.  The problem is to allocate EPA resources of equipment and technicians to clean up two Superfund sites, one in Worcester the other in Boston.  Each site has unique characteristics that require different combinations of equipment (soil reclamation machines) and technicians (site reclamation specialists).  The different combinations are given in the following table. Note that the requirements are given in resource hours required per ton cleaned at each site.  It takes 12 technician-hours and 2 machine-hours to clean a ton of waste at the Worcester site, but 10 technician-hours and 1 machine-hour to clean a ton of waste at the Boston site. The last column in the table gives to total amount of resources that the Administrator can allocate in this budget cycle.

 

 

Resource	Worcester	Boston	Total Amount Available
Technician Hours	12 hours/ton	10 hours/ton	120 hours
Machine Hours	2 hours/ton	1 hours/ton	16 hours

 

1.       The Administrator initially would like to know how to allocate resources so as to clean the largest amount of land (in tons).  Help him with this, how much should be cleaned at each site, how much of each resource should be allocated to each of the Superfund sites?  Are all the resources used?

 

To Solve this use the following method:

1.       State what is necessary for a problem to be solvable by linear programming.

After your model is built we will make sure that you have met this step.

 

2.       Formulate a mathematical model of the unstructured problem.

Perform the 5 steps in order:

Step 1.  Summarize the problem and give a table of resources and units of utility

2.  Continue with steps 2 thru 5 as required

3.  Finally state the entire model and make certain that it meets all requirements to be solved as a LP

 

3.       Solve the model.

1. On graph paper solve the problem
2. When you are done in a table give the results for utility and resource use.

 

Write-up

1.        Neatly type up or write-up the steps indicated above and provide graphs for the solution.  Label each step as it is being performed and provide summary tables where necessary, especially the final results.

2.        Discussion: What if anything did you learn here both from the standpoint of the technique as well as your results?  How satisfied are you with the results and methodology?  What further work might be done, what kind of sensitivity analysis might be performed?

3.        Title Page: Your name, course, date… on last sheet facing outwards

Due Following Tuesday