At a machine tool plant, five jobs must be completed each day. The time it takes to do each job depends on the machine used to do the job. If a machine is used at all, there is a setup time required. The relevant times are given in the table below (x means the job cannot be processed on the machine). The company's goal is to minimize the sum of the setup and machine operation times needed to complete all jobs. Jobs Machine setup Machine 1 2 3 4 5 Time (mins) 1 X 60 55 42 X 60 2 X 45 95 X 68 30 3 35 60 X X X 50 4 60 X X X 55 20 5 X X 35 X 75 40 a. Formulate as an integer program. b. Model the requirement that at least 2 machines are selected. c. Model the requirement that machines 2 and 4 cannot be both selected. d. Model the requirement that machine 1 is selected unless the total setup time is at least 90.