Ozark University admission office is processing freshman applications for the upcoming academic year. The applications fall into three categories: in-stale, out-of-state, and international. The male-female ratios for in-state and out-of-state applicants are 1:1 and 3:2, respectively. For international students, the corresponding ratio is 8:1. The American College Test (ACT) score is an important factor in accepting new students. The statistics gathered by the university indicate that the average ACT scores for in-state, out-of-state, and international students are 27, 26, and 23, respectively. The committee on admissions has established the following desirable goals for the new freshman class:
(a) The incoming class is at least 1200 freshmen.
(b) The average ACT score for all incoming students is at least 25.
(c) International students constitute at Least 10% of the incoming class.
(d) The female-male ratio is at least 3:4.
(e) Out-of-state students constitute at least 20% of the incoming class.
Formulate the problem as a goal programming model.