1.3_Tutorial_Exercises_Solution

1.3_Tutorial_Exercises_Solution - Topic 1 Linear...

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Topic 1: Linear Programming ---Reference Solution Chapter 3 Q25 Let x 1 = no. of telephone interviewers, x 2 = no. of personal interviewers Minimize Z = 50 x 1 + 70 x 2 subject to 80 x 1 + 40 x 2 3,000 (minimum number of interviews) 80 x 1 1,000 (minimum number of interviews by telephone) 40 x 2 800 (minimum number of interviews by person) x 1 , x 2 0 (non-negativity) Q26,27 a. Sensitivity range for the daily cost of a telephone interviewer: [0, 140] Sensitivity range for the number of personal interview: [0 , 2000] b. As the surplus of telephone interview is 1200, that means the firm conducts extra 1200 telephone interviews. As the surplus of personal interview is 0, no more personal interview has been conducted than the minimum requirement. c. Since the increase in the number of personal interviews is 400 which is within the allowable increase (1200), the dual price remains unchanged. (i.e. for each additional number of perosnal interview, the cost would increase by $1.125) The new cost will be 3225(=2775 + 400 (1.125)) d.
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