(1) A school district is hiring math teachers for two different high schools in their region. Each of the 6 job applicants can only work at one of the two high schools (but not both). Each school must have at least one teacher that can teach each of the following subjects: Algebra, Geometry, Trigonometry, and Calculus. Each school must have at least 2 new teachers in total. Applicant 1 and 2 are best friends, and want to work together (if they are hired at all), and applicant 5 and 6 are mortal enemies, and refuse to work at the same school. The capabilities of each applicant, and their yearly salary (in thousands of dollars) is given in the table below. - App 1 App 2 App 3 App 4 App S App 6 Algebra | Geometry | Yes ' | Yes | Yes | | Yes | Trig | ' Yes | Yes | Yes | Yes | | Calculus Formulate an integer programming problem to minimize the total cost for the school. (Do NOT solve - just formulate!)