Please answer in less than 24 hours this is all one question.

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 Interview time per student 12 minutes 10 minutes 13 minutes 9 minutes McLellan charges $3.00 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. 11 minutes 16 minutes Let T, B, H, A, M, S represent the number of students interviewed in Technology, Business, Health, Arts & Sciences, Media, and Social Services respectively. OBJECTIVE FUNCTION Minimize Cost = Type your objective function in the following box: (12%) CONSTRAINTS IGNITE requires that McLellan satisfies the following constraints. Type each constraint in the box below it. C: Interview at least 32 students in Media. C: Interview no less than 23 Arts & Sciences students. C: Interview a minimum of 300 students in total. C3: Interview at most 93 students in Business and Arts & Sciences combined. (6%) (6%) C6: (6%) Interview a maximum of twice as many Social Services students as Technology Cs: students. (6%) C10: (10%) The number of Business students interviewed should not exceed that of Arts & Sciences students by more than 12. (10%) Cr: The number of Health students interviewed should not be above 30% of all students interviewed. (10%) The total number of Social Services and Health students interviewed (combined) should be at least 33% of all students interviewed. (10%) Cg: Total interview time for Media and Social Services students combined should be at least 3.25 hours. (12%) Total interview time for Technology students should not be above 28% of the interview time for Arts & Sciences and Health students combined. (12%)