Models with integer variable problem

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P6-40 QUESTION:
You are given a group of possible investment projects for your company’s capital. For each project, ou are given the NPV the project would add to the firm,as well as the cash outflow required by each project during each year. Given the information above, determine the ivnestments 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.

Capital budgeting            
            
Note: All cash amounts are in $millions.            
            
Cash outflows in various years, NPV of projects            
 Project 1 Project 2 Project 3 Project 4 Project 5 Project 6 Project 7 Project 8 Project 9 Project 10 Project 11 Project 12
Year 1 $1 $3 $4 $6 $5 $4 $2 $0 $1 $3 $9 $8
Year 2 $3 $4 $4 $5 $1 $5 $3 $0 $1 $2 $2 $7
Year 3 $4 $2 $3 $3 $2 $2 $1 $3 $4 $4 $4 $1
Year 4 $1 $1 $2 $2 $3 $5 $4 $6 $8 $1 $1 $1
Year 5 $1 $2 $1 $3 $8 $5 $6 $7 $3 $6 $1 $1
NPV $20 $25 $30 $35 $40 $42 $31 $33 $35 $37 $38 $39
            
Selected projects (1 if selected, 0 if not)            
 Project 1 Project 2 Project 3 Project 4 Project 5 Project 6 Project 7 Project 8 Project 9 Project 10 Project 11 Project 12
            
            
Budget constraints            
 Outflow  Budget         
Year 1            
Year 2            
Year 3            
Year 4            
Year 5            
            
Total NPV            

              
P6-44 QUESTION:
QUESTION: To graduate from Souteastern 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 fulfull more than one requirement: Calculus can fulfill the math requirement; 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 requirements.Some courses have prerequisites for others: Calculus is a prerequisite for Business Statistics; Intro to Computer Programming is a prerequisite for Computer Simluation and for Data Structures; 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 contraint that ensures that the changing cell for Calculus is greater than or equal to the changing cell for Business Statistics)            

Choosing college courses       
       
Requirements (along side) that are met by taking available courses (along top) (1 if it fills reqt, 0 if not)       
 Calculus OR Data Structures Bus Stats Simulation Intro to Comp Prog Forecasting
OR       
Math       
Computer       
       
 Calculus OR Data Structures Bus Stats Simulation Intro to Comp Prog Forecasting
Course taken       
       
Prerequisite constraints       
     (Calculus for Bus Stats)  
     (Intro to Comp Prog for Simulation)  
     (Intro to Comp Prog for Data Structures)  
     (Bus Stats for Forecasting)  
       
Major requirement constraints       
 Courses taken  Required    
OR       
Math       
Computer       
       
Total courses       

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