please make sure to answer all questions specially e, f, and g.

Question #3. (5 Marks) 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