(20 Points) Hogwarts University admissions office is processing applications for the upcoming academic year. The applications fall into three categories: in-state, out-of-state, and international. The male-female ratios for in-state, and out-of-state applications are 1:1 and 3:2, respectively. For the international students, the corresponding ratio is 8:1. The ACT score is an important factor in accepting new students. Statistics 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 this problem as a goal programming model