Integer Programming

Integer Programming

A workshop has 6 machines that can perform any job assigned to them. The workshop has 10 jobs that it 
needs to complete over two days. Jobs 1 to 5 must be finished on the first day and jobs 6 to 10 must be 
finished on the second day. Any of the machines will take a complete day to finish any of the jobs. The 
workshop manager requires that none of the machines stay idle for the two days. Write an integer 
programming model that would minimize the total costs of running the 10 jobs. The cost per job per 
machine is given in Table 2. 
Table 2 
Job 1 Job 2 Job 3 Job 4 Job 5 Job 6 Job 7 Job 8 Job 9 Job 10 
Machine 1 $85 $75 $80 $65 $80 $90 $85 $55 $60 $100 
Machine 2 $82 $76 $78 $63 $80 $85 $82 $54 $58 $90 
Machine 3 $87 $77 $82 $60 $82 $90 $87 $54 $62 $102 
Machine 4 $79 $72 $76 $59 $78 $85 $77 $53 $56 $90 
Machine 5 $90 $78 $84 $70 $85 $93 $90 $57 $64 $97