The admissions office at Tech wants to determine how many in-state and how many out-of-state students to accept for next fall’s entering freshman class. Tuition for an in-state student is $7,600 per year, whereas out-of-state tuition is $22,500 per year. A total of 12,800 in-state and 8,100 out-of-state freshmen have applied for next fall, and Tech does not want to accept more than 3,500 students. However, because Tech is a state institution, the state mandates that it can accept no more than 40% out-of-state students. From past experience the admissions office knows that 12% of in-state students and 24% of out-of-state students will drop out during their first year. Tech wants to maximize total tuition while limiting the total attrition to 600 first-year students.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.