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 the

m $

7

.

0

0 to survey first year and sophomore residential students and $

9

.

0

0 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

.

50

for junior an

d seniors. For statistical validity they want to

interview at least

10

00 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 st

udents, this is 30% of the combination of the two types of first year students should be

distance first year students)

At least 2

5

% of sophomore students surveyed should be distance students

At least

3

0

% of junior students surveyed should be distance

students

At least

4

0% of senior students surveyed should be distance students

No more than

2

5

% of all the students surveyed should be first year students

Juniors and seniors should be at least 4

0

% of the students surveyed

Each

of the eight types of student

s 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 no

n

-

negativity).

Questions:

a)

If the cost of surveying first year and sophomore residential students increases from $

7.0

0

to

$

8

.

5

0

-

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?