Klien Research has been hired to survey cable television customers to determine their attitudes toward a restructuring of the basic cable service and rate schedule. The cable company wants to classify participants according to whether or not there are children under the age of 16 in the household and as to whether or not the household subscribes to any premium channels.
The basic cost of conducting an interview is $5. Those households with children under 16 are asked a second series of questions which adds an additional cost of $4 to their interviews. Households with premium channels are questioned about their viewing habits, and this adds an additional $3 to the cost of their interviews. Cost is to be minimized.
The cable company wants responses from at least 50 customers. Premium subscribers should constitute at least half of the customers surveyed. At least 60% of households surveyed should have children under 16. Of those households with children under 16, no more than half should be premium subscribers.
Develop a linear programming model for this problem.