A school is offering two courses; history and science. The history class size is 10 students. The science class size is 15 students.

The history course is 16 lectures and the science course is 12 lectures.

Students who join a class must attend 2 lectures per week.

Teachers can do 1,2 or 3 lectures in one day.

The teacher wage for 1 class is $20, for 2 classes on the same day is $43 and for 3 classes on the same day is $75. The teachers cannot do more than 3 classes per day.

Each teacher should deliver a minimum of 9 classes per week.

Assuming we have 240 students, how many teachers should we hire to minimize the cost?