An academic computing center receives a large number of jobs from students and faculty to be executed on the computing facilities. Each student job requires 6 units of space on disk, and 3 units of time on a printer. Each faculty job requires 8 units of space on disk, and 2 units of time on a printer. A mixture of jobs is to be selected and run as a batch, and the total disk space and printer time available for a batch are 48 units and 60 units, respectively. The computer center is paid three times as much for running a student job as for running a faculty job. a) Formulate a linear programming problem to determine the mixture of jobs to be run as a batch that will maximize computer center income. Clearly define your decision variables, objective function and constraints b) Find the optimal solution using the graphical method c) Using manual sensitivity analysis, determine the range over which the revenue per student job can change without changing the optimal solution d) Using manual sensitivity analysis, determine the range over which the revenue per faculty job can change without changing the optimal solution e) Based on your graphical solution, if you can acquire additional disk space or printer time, which one would you acquire and why?