The MakeIt Public Relations firm has been contracted to do a survey following an

Question

The MakeIt Public Relations firm has been contracted to do a survey following an election. The
firm must assign interviewers to conduct the survey. The interviews are to be conducted by
telephone and in person. One person can conduct 80 telephone interviews or 40 personal
interviews in a single day. The following criteria have been established by the firm in order to
ensure a representative survey:
At least 3,000 interviews must be conducted.
At least 1,000 interviews must be by telephone.
At least 800 interviews must be personal.
Due to urgency of the project, the interviews must be conducted within one day. An interviewer
conducts only one type of interview on the day. The cost is $50 per day for a telephone interviewer
and $70 per day for a personal interviewer. The firm wants to know the number of interviewers to
hire in order to minimize the total cost of the survey.

a) Formulate a linear programing model for this problem.

b) Solve the problem using Excel. (Fractional solution is accepted)

c) Based on the optimal solution, does the firm conduct any more telephone or personal
interviews than are required, and if so, how many more?

d) What would be effect on the optimal solution if the firm was required by the client to
increase the number of personal interviews conducted from 800 to a total of 1,200?

Explanation / Answer

(a)

LPP Formulation:

Let x be number of telephone interviewer and y be the number of personal interviewer to be hired.

Minimize Cost = 50x + 70y
subject to,
80x + 40y >= 3000
80x > = 1000
40y >= 800

(B)

Solver

(C)

The firm conducts 2200 telephonic and 800 personal interview to meet the target. This means 2200-1000 = 1200 extra telephonic interviews were conducted.

(D)

If the minimum number of personal interviews to be conducted are increased from 800 to 1200. Then values of x and y for optimal solution would be x = 1800 and y=1200

The minimum cost will be $3225 compared to $2775 earlier.

Solver Solution x y Total Demand Decision Variables 27.5 20 Cost 50 70 2775 Constraint 1 80 40 3000 3000 Constraint 2 80 0 2200 1000 Constraint 3 0 40 800 800

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