M5.3A 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 $7.00 to survey first year and sophomore residential students and $9.00 to survey junior and senior residential students. The cost to interview distance students is slightly higher. It will cost $7.50 for first year and sophomores and $9.50for junior and seniors. For statistical validity they want to interview at least 1000 students. They feel that there are certain criteria that they must adhere to:

At least 30% of first year students surveyed should be distance students (Hint: this is not 30% of all students, this is 30% of the combination of the two types of first year students should be distance first year students)

At least 25% of sophomore students surveyed should be distance students

At least 30% of junior students surveyed should be distance students

At least 40% of senior students surveyed should be distance students

No more than 25% 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 8% of the total interviews(Hint:

this is 8 separate constraints)

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.

SOLUTION: The optimal solution, the value of the cost, should be $7,963.75. Some of your decision variables might not be integers -this

is OK. You should have a total of 15 constraints (not including non-negativity).

Questions:

a)If the cost of surveying first year and sophomore residential students increases from $7.00 to $8.50 -what is the new minimum cost in your optimal solution?

b)If your survey required that at least 15% of the students in the survey must be residential senior students -what is the new minimum cost in your optimal solution?