A student project at WCU was initiated to try to determine the impact of implementation of new technologies. The students want to survey both distance and residential undergraduate students in the four different years at Western (first year, sophomore, junior, and senior).
They have estimated that it will cost them $5.50 to survey first year and sophomore residential students and $8.00 to survey junior and senior residential students. The cost to interview distance students is slightly higher.
It will cost $6.75 for first year and sophomores and $9.50 for junior and seniors. For statistical validity they want to interview at least 900 students.
They feel that there are certain criteria that they must adhere to:
- At least 25% of first year students surveyed should be distance students
- At least 20% of sophomore students surveyed should be distance students
- At least 35% of junior students surveyed should be distance students
- At least 40% of senior students surveyed should be distance students
- No more than 35% of all the students surveyed should be first year students
- Juniors and seniors should be at least 45% of the students surveyed
- Each of the eight types of students must be represented in the survey by at least 10% of the total interviews
Formulate and solve this problem in Excel to determine the number of each type of student that should be surveyed that meets the requirements and minimizes the cost to carry out the interviews.
a) What is the minimum cost in your optimal solution (the value of the objective function)?
b) If the cost of surveying first year and sophomore residential students increases from $5.50 to $7.00- what is the new minimum cost in your optimal solution?