Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 34

Solve the linear programming model formulated in Problem for Rucklehouse Public Relations graphically.
a. Determine the sensitivity ranges for the daily cost of a telephone interviewer and the number of personal interviews required.
b. Does the firm conduct any more telephone and personal interviews than are required, and if so, how many more
c. What would be the 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
Problem
Rucklehouse Public Relations has been contracted to do a survey following an election primary in New Hampshire. The firm must assign interviewers to conduct the survey by telephone or 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 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.
An interviewer conducts only one type of interview each 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 minimum number of interviewers to hire in order to minimize the total cost of the survey.
Formulate a linear programming model for this problem.