EXERCISE $9\mathrm{.}8$ from DMD textbook$$textbook $($Data$,$ Models, and Decisions: The Fundamentals of Management Science by Dimitris

Bertsimas and Robert M$.$ Freund, Dynamic Ideas LLC$,2004$

Linda Johansen, an incoming first$-$year MBA student, would like to determine her course schedule for her first two semesters of business school. Linda has created a list of twenty potential courses that most interest her, shown in Table $9\mathrm{.}25.$ Linda has ranked her interest in each of these courses as a number between $3$ and $5,$ as shown in the fifth column of Table $9\mathrm{.}25.$

Linda is allowed to take at most five courses in each semester. In determining her course schedule, Linda needs to consider the following:

$$ Linda can only take a course if she has completed or is concurrently taking all courses that are prerequisites for the course. The prerequisites for all twenty courses are shown in the fifth column of Table $9\mathrm{.}25.$

$$ In the Fall term, Linda must take at least three of the following five courses: Quantitative Methods $($course $1),$ Microeconomics $($course $2),$ Finance Theory $($course $3),$ Accounting I $($course $6),$ and Business Communications $($course $20).$

$$ If Linda takes Financial Engineering $($course $8),$ she will not be allowed to take Options and Futures $($course $14),$ because these two courses cover fairly similar material.

$$ Linda would like to take at least one course in Marketing $($courses $12$ and$/$ or $13),$ and at least one course in Operations Management $($courses $10$ and$/$ or $11).$

Suppose that Linda's overall objective is to maximize her total interest level.

$($a$)(6$ points$)$ Construct and solve a discrete optimization model that can be used to determine Linda's optimal course schedule. What is the optimal course schedule?

$($b$)(3$ points$)$ Try to amend your model in order to generate a different solution with the same $($optimal$)$ objective value. What is the other optimal course schedule?

Course number Course Title Semester Offered Course Prerequisites Interest Level

$1$ Quantitative Methods F $5$

$2$ Microeconomics F $5$

$3$ Finance Theory F$/$S $4$

$4$ Strategy I F $4$

$5$ Strategy II S $44$

$6$ Accounting I F $3$

$7$ Accounting II S $2,63$

$8$ Financial Engineering S $1,35$

$9$ Statistics S $14$

$10$ Operations Management I F $4$

$11$ Operations Management II S $1,104$

$12$ Marketing I F $3$

$13$ Marketing II S $9,123$

$14$ Options and Futures S $35$

$15$ Information Technology I F $4$

$16$ Information Technology II S $154$

$17$ Entrepreneurship S $44$

$18$ New Product Development S $10,12,173$

$19$ Organizational Processes F $43$

$20$ Business Communications F $5$

Table $9\mathrm{.}25$ The twenty courses that Linda is most interested in taking in her first year of business school