Sandy Arledge will soon start an accelerated MBA program at the University of South Chicago (USC). USC follows a similar bidding system to what you use at Booth, and Sandy wants to come up with a plan for what courses she would take and when. The accelerated MBA is a two-quarter program (called as quarters A and B). USC offers 15 courses, each course is offered in both quarters, and for each of these courses USC has published the historical average of the bid points. Sandy has also attempted to quantify how much utility she would get from each of the courses based on her career goals and skill set. Both of these numbers, and the list of the 15 courses as well as their pre-requisites are in the table below. Utility Pre-requisites (P=Past, PC=Past or Concurrent) Courses 1. Business Statistics 2. Applied Regression 3. Accounting 4. Microeconomics 5. Managing in Orgs. 6. Investments 7. Portfolio Mgmt. 8. Corporation Fin. 9. Cases in Fin. Mgmt. 10. Managerial Dec. Modeling 11. Marketing Strategy 12. Negotiations 13. Competitive Strategy 14. Operations Mgmt. 15. Quantitative Marketing 1 3 3 4 9 4 7 5 10 5 4 4 6 7 8 Bid points 0 300 100 400 2500 200 300 500 1000 350 1000 1100 1000 800 1500 Accounting (P) Accounting (P), Investments (PC) Corporation Fin. (P) Microeconomics (P) Microeconomics (P) Business Statistics or Applied Regression (P), Marketing Strategy (PC) (Example: To take Portfolio Mgmt. in the current quarter, Sandy must have taken Accounting in a prior quarter, and must have taken Investments in a prior quarter or must be taking it in the current quarter.) The bidding system works as follows: Students begin with 4000 bid points, and get 1000 bid points for ev- ery course they complete. Therefore, the maximum bid points they can spend in quarter A is 4000. Sup- pose they spend 2800 bid points in quarter A and take 3 courses, they will have 4000-2800+3x 1000 = 4200 bid points to spend in quarter B. For the sake of planning, Sandy will assume that the historical average is a good estimate of how many points she will need to spend to register for these courses (irrespective of the quarter). USC enforces the following degree requirements: 1. The total number of courses taken must be no less than 8, and no more than 9. 2. In each quarter, the number of courses taken must be no less than 3, and no more than 5. 3. The student must take Microeconomics and Accounting. take at least one of Business Statistics or Applied Regression. take at least one of Marketing Strategy or Competitive Strategy. 6. take at least one of Operations Mgmt. or Managerial Dec. Modeling. Sandy would like to determine a utility maximizing schedule of courses for the two quarters, subject to the bid point constraints, the degree requirements, and the course prerequisites. Your goal is to write an optimization model with binary decision variables to solve Sandy's problem. You can only write constraints which are linear in the decision variables. 4. 5.