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IGNITE, a student life group at a prominent college, is considering hiring McLellan Consulting to conduct a survey geared towards evaluating the effects of mandatory remote learning on students during the wave of the COVID-19 pandemic. The survey will be carried out by telephone interview. Due to the uniqueness of programs offered by the different faculties at the college, McLellan's survey design requires allocating different amounts of time per student interviewed in different faculties. The amount interview time required per student in each faculty is given in the following table: Faculty Technology Business Health Arts & Sciences Media Social Services DECISION VARIABLES McLellan charges $2.00 per minute for interviews. IGNITE's objective is to minimize interview costs (in dollars) and you have been tasked with formulating a linear programming model for the student body. OBJECTIVE FUNCTION Let T, B, H, A, M, S represent the number of students interviewed in Technology, Business, Health, Arts & Sciences, Media, and Social Services respectively. Minimize Cost = CONSTRAINTS Interview time per student 12 minutes 10 minutes Type your objective function in the following box: 14 minutes 11 minutes 12 minutes 17 minutes IGNITE requires that McLellan satisfies the following constraints. Type each constraint in the box below it. C₁: Interview no less than 34 students in Business. C₂: Interview a minimum of 40 Media students. C₁: C₁: Interview at most 285 students in total. C₂: C₁: Interview no more than 82 students in Social Services and Business combined. (6%) Cui Ci: (6%) (6%) C₁: Interview at least three times as many Health students as Technology students. (10%) (6%) Cr: The number of Arts & Sciences students interviewed should not be above 27% of all students interviewed. The number of Social Services students interviewed should not be below that of Business students by more than 8. (10%) (10%) The total number of Health and Arts & Sciences students interviewed (combined) should be minimum 34% of all students interviewed. (12%) Total interview time for Business and Health students combined should be minimum 3 hours (12%) Total interview time for Technology students should be at most 29% of the interview time for Media and Arts & Sciences students combined (128)