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:

FacultyInterview time

per studentTechnology9 minutesBusiness7 minutesHealth11 minutesArts & Sciences6 minutesMedia9 minutesSocial Services13 minutes

McLellan charges $2.50 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.

DECISION VARIABLES

LetT

T

,B

B

,H

H

,A

A

,M

M

,S

S

represent the number of students interviewed in Technology, Business, Health, Arts & Sciences, Media, and Social Services respectively.

OBJECTIVE FUNCTION

Type your objective function in the following box:

Minimize Cost =(12%)

CONSTRAINTS

IGNITE requires that McLellan satisfies the following constraints.

Type each constraint in the box below it.

C

1

:

C1:

Interview at least 40 students in Technology.(6%)

C

2

:

C2:

Interview a maximum of 24 Social Services students.(6%)

C

3

:

C3:

Interview no less than 83 students in Business and Technology combined.(6%)

C

4

:

C4:

Interview no more than 285 students in total.(6%)

C

5

:

C5:

Interview a minimum of twice as many Health students as Media students.(10%)

C

6

:

C6:

The number of Business students interviewed should not exceed that of Technology students by more than 7.(10%)

C

7

:

C7:

The number of Arts & Sciences students interviewed should not be above 21% of all students interviewed.(10%)

C

8

:

C8:

The total number of Health and Arts & Sciences students interviewed (combined) should be no less than 23% of all students interviewed.(10%)

C

9

:

C9:

Total interview time for Technology and Health students combined should be no less than 2.25 hours.(12%)

C

10

:

C10:

Total interview time for Media students should be no more than 29% of the interview time for Social Services and Arts & Sciences students combined.(12%)