Problem 1:

You are given a group of possible investment projects for your company's capital. For each project, you are given the NPV the project would add to the firm, as well as the cash outflow required by each project during each year. Determine the investments that maximize the firm's NPV. The firm has $30 million available during each of the next five years. All numbers are in millions of dollars.

Problem 2:

To graduate from Southeaster University with a major in operations research (OR), a student must complete at least two math courses, at least two OR courses, and at least two computer courses. Some courses can be used to fulfill more than one requirement: Calculus can fulfill the math requirements; Operations Research can fulfill the math and OR requirements; Data Structures can fulfill the computer and math requirements; Business Statistics can fulfill the math and OR requirements; Computer Simulation can fulfill the OR and computer requirements; Introduction to Computer Programming can fulfill the OR and math requirement; and Forecasting can fulfill the OR and math requirements. Some courses are prerequisites for others: Calculus is a prerequisite for Business Statistics: Introduction to Computer Programming is a prerequisite for Computer Simulation and for Data Structure; and Business Statistics is a prerequisite for Forecasting. Determine how to minimize the number of courses needed to satisfy the major requirements. (Hint: Because Calculus is a prerequisite for Business Statistics, for example, you will need a constraint that ensures that decision variable for Calculus is greater than or equal to the decision variable for Business Statistics.)