The admissions office at State University wants to develop a planning model for next year€™s entering freshman class. The university has 4,500 available openings for freshmen. Tuition is $8,600 for an in-state student and $19,200 for an out-of-state student. The university wants to maximize the money it receives from tuition, but by state mandate it can admit no more than 47% out-of-state students. Also, each college in the university must have at least 30% in-state students in its freshman class. In order to be ranked in several national magazines, it wants the freshman class to have an average SAT score of 1150. Following are the average SAT scores for last year€™s freshman class for in-state and out-of-state students in each college in the university plus the maximum size of the freshman class for each college:

a. Formulate and solve a linear programming model to determine the number of in-state and out-of-state students that should enter each college.
b. If the solution in (a) does not achieve the maximum freshman class size, discuss how you might adjust the model to reach this classsize.

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Average SAT Scores College 1. Architecture 2. Arts and Sciences 3. Agriculture 4. Business 5. Engineering 6. Human Resources In-State Out-of-State Total Capacity 1350 1010 1020 1090 1360 1460 1050 1110 1180 1420 1400 470 1,300 240 820 1,060 610