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 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:

Average SAT Scores College In-State Out-of-State Total Capacity 1. Architecture 1350 1460 470 2. Arts and Sciences 1010 1050 1,300 3. Agriculture 1020 1110 240 4. Business 1090 1180 820 5. Engineering 1360 1420 1,060 6. Human Resources 1000 1400 610

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 class size. LO.1