A Media & Public Relations company has been contracted to do a survey following the launching of a new product at Jubail. 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.
a. [1 Mark] Formulate a linear programming model for this problem.
b. [1 Mark] Solve the problem using software and show the output.
c. [0.5 Mark] Determine the sensitivity ranges for the daily cost of a telephone interviewer and the number of personal interviews required.
d. [0.5 Mark] Does the firm conduct any more telephone and personal interviews than are required, and if so, how many more?
e. [0.5 Mark] 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?
f. [1 Mark] If the firm could reduce the minimum interview requirement for either telephone or personal interviews, which should the firm select? How much would a reduction of one interview in the requirement you selected reduce total cost?
g. [0.5 Mark] Identify the sensitivity ranges for the cost of a personal interview and the number of total interviews required.