Klein Research has been hired to survey cable television customers to determine
ID: 389441 • 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 premium channels. The basic cost of conducting an interview is $5. 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 $3 to the cost of their interviews. The cost structure is shown in the following table Without premium channels With premium channels Without children under 16 With children under 16 12 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% of the 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.Explanation / Answer
2) 3rd (Min 5x11 + 8x12 + 9x21 + 12x22)
The objective is to have minimum cost
X11 = Without under 16 and Without premium
X12 = without under 16 with premium
X21 = With under 16 without premium
X22 = With under 16 with premium
So, the function will be sum product of cost and value for each cell
3) 4th (x11 + x12 + x21 + x22 >= 500)
The constraint is to obtain minimum 500 responses. Hence, the sum of all the options must add up to 500 at least
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