Problem: A student project at Columbia 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 CU (first year, sophomore, junior, and senior). They have estimated that it will cost them $5.00 to survey first year and sophomore residential students and $7.50 to survey junior and senior residential students. The cost to interview distance students is slightly higher. It willcost $6.50 for first year and sophomores and $8.75 for junior and seniors. For statistical validity they want to interview at least 1000 students. They feel that there is certain criteria that they must adhere to: 

• At least 20% of first year students surveyed should be distance students
• At least 25% of sophomore students surveyed should be distance students
• At least 40% of junior students surveyed should be distance students
• At least 30% of senior students surveyed should be distance students
• No more than 30% of all the students surveyed should be first year students
• Juniors and seniors should be at least 40% of the students surveyed
• Each of the eight types of students must be represented in the survey by at least 7% of the total interviews

Formulate and solve this problem in Excel (and run a sensitivity analysis) 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) Are there alternate optimal solutions for this problem?