Can someone verify my answer to one part of this linear programming problem?

Can someone help me to set up this linear programming question?


I don't need you to solve it but I would like you to set up its linear programming model for me since the only thing that I got stuck with this problem is I am unable to transfer the given information into mathematical terms. Many thanks in advance.





The question is as follows:





Brenda, a university student, is considering seven 3 credit hour courses which are shown on the following table. Also included are the average number of hours she expects to have to devote to each course each week and her minimum expected grade in each course.





Courses Average Hours per week Minimum Grade.


Management. 5 B


Principles of Accounting. 10 C


Corporate Finance. 8 C


Quantitative Methods. 12 D


Marketing Management. 7 C


C Programming. 10 D


English Literature. 8 B





Edit: The table is out of format when I copy and posted it onto yahoo answers from excel. Numbers under the column titled "Average hours per week" of the table are the average hours per week for each corresponding course. Similarily, Letters under the next column titled "Minimum grade" of the table are the minimum grades for each corresponding course.








An A in a course earns 4 quality credits per hour, a B earns 3 quality credits, a C earns 2 quality credits, a D earns 1 quality credits, and a F earns no quality credit per hour. Brenda wants to select a schedule that will provide at least a 2.0 grade point average. She must take at least 12 credit hours. Brenda would like to take no more than two of these courses: Principles of Accounting, Corporate Finance, Quantitative methods and C programming. She needs to take at least three of the following courses: Management, Principles of accounting, C programming, and English. Brenda wants to develop a course schedule that will minimise the number of hours she has to work each week.





Required:


Formulate a 0-1 integer linear programming model for this problem.





MY ANSWER:


Let x1=Management, x2=Principles of Accounting, x3=Corporate Finance, x4=Quantitative Methods, x5=Marketing Management, x6=C Programming, x7=English Literature where x1,x2,x3,x4,x5,x6 and x7 = 0 or 1.





The GPA constraint for this problem is


(3x1+3x2+3x3+3x4+3x5+3x6+3x7)/(3*7)%26gt;= 2.0


3(x1+x2+x3+x4+x5+x6+x7)/21%26gt;=2.0


(x1+x2+x3+x4+x5+x6+x7)%26gt;= 14|||While setting up an LP, it is important to identify two things clearly:


the objective function - here it is to minimize course hours


and the constraints - here they are related to GPA, minimum credit hours required and course constraints...





Considering this, we can set up an LP as follows





Taking the variables as you have:





the objective function would be:


Minimize: 5x1 + 10x2 + 8x3 + 12x4 + 7x5 + 10x6 + 8x7





The constraints:


Credit Hours:


3 ( x1 + x2 + x3 + x4 + x5 + x6 + x7 ) %26gt;= 12


or x1 + x2 + x3 + x4 + x5 + x6 + x7 %26gt;= 4





Min GPA:


3x1 + 2x2 + 2x3 + 1x4 + 2x5 + 1x6 + 3x7 %26gt;= 2.0 (x1 + x2 + x3 + x4 + x5 + x6 + x7 )


or x1 - x4 - x6 + x7 %26gt;= 0





Course Constraints:


x2 + x3 + x4 + x6 %26lt;= 2


and


x1 + x2 + x6 + x7 %26gt;= 3





HTH!





P.S. Do pick a best answer.|||Looks as if the GPA constraint is wrong.

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