An organization conducts marketing research to learn about consumer characteristics, attitudes, and preferences. Marketing research firms that specialized in providing such information often do the actual research for client organizations. Typical services offered by a marketing research firm include designing the study, conducting market surveys, analyzing the data collected, and providing summary reports and recommendations for the clients. In the research design phase, targets or quotas maybe established for the number and types of respondents to be surveyed. The marketing research firm's objective is to conduct the survey so as to meet the client's needs at a minimum cost.
Market Survey, Inc. (MSI), specializes in evaluating consumer reactions to new products, services, and advertising campaigns. A client firm requested MSI's assistance in ascertaining consumer reaction to a recently marketed household product. During meetings with the client, MSI agreed to conduct door- to- door personal interviews to obtain responses from households with children and households without children. In addition, MSI agreed to conduct both day and evening interviews. Specifically, the client's contract called for MSI to conduct 1000 interviews under the following quota guidelines:
a) Interview at least 400 households with children.
b) Interview at least 400 households without children.
c) The total number of households interviewed during the evening must be greater than or equal the number of households interviewed during the day.
d) At least 40% of the interviews for households with children must be conducted during the evening.
e) At least 60 percent of the interviews for households without children must be conducted during the evening.
Because the interviews for the households with children take additional interviewer time and because evening interviewers are paid more than day time interviewers, the cost varies with the type of interview. Based on previous research studies, estimate of the interview costs are as follows:
|
Interview Cost
|
|
|
Household
|
Day
|
Evening
|
|
Children
|
$20
|
$25
|
|
No Children
|
$18
|
$20
|
Formulate and solve a linear programming model that will answer the following question:
What is the household and the time of the day interview plan that will satisfy the contract requirements at a minimum total interviewing cost?