Problem 3 (25 Points) A University would like to optimize student preferences fo

Question

Problem 3 (25 Points) A University would like to optimize student preferences for the selection of elective courses. Consider the following case of 10 students who are required to select two courses out of six offered electives. The table below gives scores that represent each student's preference for individual courses, with a score of 100 being the highest. For simplicity, it is assumed that the preference score for a two-course selection is the sum of the individual score. Course capacity is the maximum number of students allowed to take the Students1 100 80 10 60 75 10 80 70 60 100 100 80 10 Course6 Formulate a linear mathematical programming model to determine the optimal solution. Clearly define your decision variables, objective and constraints). a) b) Use Excel and Solver to implement and solve the model you formulated in part (a) to find the optimal solution. Report your results in the report by including a snapshot of your spreadsheet solution

Explanation / Answer

a)The decision variables is defined x(i,j) where i represents the student number from 1 to 10 and j represents the course from 1 to 6. x(i,j) is binary variable taking value of either 0 or 1 depending on whether the particular course is selected by that student. Thus we have a total of 60 variables.

We will denote the preference score by p(i,j) which is given.

The objective function is to maximize summation[x(i,j)*p(i,j)] for all i and j.

Constraints:-

The sum of rows has to be equal to 2 as maximum elective is 2. thus summation[x(i,j)]=2 for only j 1 to 6, but for every row.

The column sum has to be equal to the capacity of the course denoted by c(j). Thus the constraint becomes

summation[x(i,j)]=cj for i 1 to 10 but for every column,

Thus we have 16 constraints.

The excel file is not attaching here but the above procedure if you follow in excel, the optimum solution will be obtained.

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