A marketing research firm has been commisioned to conduct a survey of households in a residential...

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A marketing research firm has been commisioned to conduct a survey of households in a residential section of the city. There are three target populations: single persons, couples with no children, and couples with children. The contract calls for conducting at least 150, 200, 300 interviews in these populations, respectively. Visits can be made either during the day or in the evening. Only a fraction of the visits are successful (i.e., find someone at home to be interviewed.) Usually households con- sider the interviews a bother, and they generate negative reactions. Evening interviews generate more intense negative reactions than the day interviews. So the company al- locates itself a penalty of 2 units for each interview conducted during the day, and 4. units for each interview conducted during the evening. They would like to see the total penalty minimized. Other data is given below. Population Single Couples, no children Couples with children Min. interviews needed Fraction of successful visits Evening 0.4 0.6 0.8 150 200 300 Day 0.1 0.2 0.4 By union regulations, the number of visits in the evening cannot exceed 80% of visits in the day. The company would like to minimize both the number of total visits, and the total penalty points for completing the contract. Formulate as a multiobjective problem ignoring the integer requirements on the variables. A marketing research firm has been commisioned to conduct a survey of households in a residential section of the city. There are three target populations: single persons, couples with no children, and couples with children. The contract calls for conducting at least 150, 200, 300 interviews in these populations, respectively. Visits can be made either during the day or in the evening. Only a fraction of the visits are successful (i.e., find someone at home to be interviewed.) Usually households con- sider the interviews a bother, and they generate negative reactions. Evening interviews generate more intense negative reactions than the day interviews. So the company al- locates itself a penalty of 2 units for each interview conducted during the day, and 4. units for each interview conducted during the evening. They would like to see the total penalty minimized. Other data is given below. Population Single Couples, no children Couples with children Min. interviews needed Fraction of successful visits Evening 0.4 0.6 0.8 150 200 300 Day 0.1 0.2 0.4 By union regulations, the number of visits in the evening cannot exceed 80% of visits in the day. The company would like to minimize both the number of total visits, and the total penalty points for completing the contract. Formulate as a multiobjective problem ignoring the integer requirements on the variables.

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