The Ozark University admission office is processing freshman 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 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 GP model.