Klein Research has been hired to survey cable television customers to determine
ID: 3040562 • Letter: K
Question
Klein Research has been hired to survey cable television customers to determine their attitudes toward a restructuring of the basic cable service and the rate schedule. The cable company wants to classify the participants according to whether or not a household has children under 16 and according to whether or not the household subscribes to any premium channels. The basic cost of conducting an interview is S5. Those households with children under 16 are asked a second series of questions that adds an additional cost of $4 to their interview. Households with premium channels are questioned about their viewing habits that adds an additional 53 to the cost of their interviews. The cost stucture is shown in the following table Without premium channels With ith under 16 The cable company wants the following to be satisfied Obtain responses from at least 500 households Premium subscribers should count for at least half of the total subscribers interviewed * At least 60% ofthe interviewed households should have children under 16. . Of those households with children under 16, no more than 30% should be premium subscribers .Among those households without children under 16, for each interviewed household without premium subscription, at least two households with premium subscription must be interviewed You are required to formulate a linear programming model to determine the number of households to be interviewed in each category so as to minimize the total cost within the restrictions of the above requirements Reasonable definitions of the decision variables are xn-household without children under 16 and without premium subscription -household without children under 16 but with premium subscription -household with children under 16 but without premium subscription -household with children under 16 and with premium subscription x11-number of interviewed households without children under 16 and withou prem um subscrption x,-number of interviewed households without children under 16 but with premium subscription -number of interviewed households with children under 16 but without premium subscription number of interviewed households with children under 16 and with premium subscription xa-cost ofterviewmg a household without children under 16 and without premium subscription x-cost of interviewing a household without children under 16 but with premium subscription -cost of interview ing a household with children under 16 but without premium subscription -cost of interviewing a household with children under 16 and with prem um subscription All of the above are reasonable definitions, None of the above.Explanation / Answer
1. The decision variables should be based on the information provided. Here the data provided is the number of families having children under 16 or not and are having premium subscription or not. Hence first option is correct.
2. In the optimal solution none of the variables can be negative hence the restriction here is that decision variables should be non negative in the optimal solution.
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