Management Sciences Associates (MSA) is a marketing and computer research firm based in New York City, that handles consumer surveys for various federal agencies. One of their clients is the Office of Economic Direction and Policies (OEDP). Periodically, OEDP conducts surveys to determine the effects of selected policies. In a survey for OEDP, MSA determines that it must fulfill several requirements in order to draw statistically valid data on a particular set of economic issues. These requirements are summarized as follows:
- Survey at least 2,300 U.S. households in total.
- Survey at least 1,000 households whose heads of household are 30 years old or younger.
- Survey at least 600 households whose heads of household are between 31 and 50 years old.
- Ensure that at least 15% of those surveyed live in a state that borders on Mexico.
- Ensure that no more than 20% of those surveyed, who are 51 or older, live in a state bordering on Mexico.
MSA decides that all surveys should be conducted in person. It estimates that the costs of reaching people in each age group and region category will vary because of travel costs, limited access hours, etc. Based on previous surveys, MSA has estimated these costs as outlined below.
COST PER PERSON SURVEYED ($)
AGE
REGION Under 30 31 - 50 Over 50
State Bordering Mexico 7.50 6.80 5.50
State NOT Bordering Mexico 6.90 7.25 6.10
MSA’s goal is to meet the five sampling requirements at the least possible cost. Formulate an appropriate mathematical problem, which, when solved, will provide the number of households in each age/region group to be surveyed, while meeting the five listed requirements at minimum total cost. (You do not need to solve the model.) Clearly define your objective and your variables.
Answer
Objective: To minimize the cost of the study while achieving the requirements set forth.
Decision Variable: The number of respondents from each age group in a state bordering Mexico or not bordering Mexico
Under 30=Y
31-50=M
Over 50=O
Bordering Mexico=B
Not Bordering Mexico=NB
X11 = number of respondents Y from B X12 = number of respondents M from B X13 = number of respondents O from B
X21 = number of respondents Y from NB X22 = number of respondents M from NB X23 = number of respondents O from NB
Subject To:
Total respondents are ? 2300
X11+ X12+ X13+ X21+ X22+ X23?2300
Total respondents Y are ? 1000
X11+ X21?1000
Total respondents M are?600
X12+ X22?600
Total respondents B is? 15% of2300
X11+ X12+ X13?2300(.15)
Total respondents NB is? 20% of O
This is what I have so far. Did I miss the mark? Do I need to add anything?
- Survey at least 2,300 U.S. households in total.
- Survey at least 1,000 households whose heads of household are 30 years old or younger.
- Survey at least 600 households whose heads of household are between 31 and 50 years old.
- Ensure that at least 15% of those surveyed live in a state that borders on Mexico.
- Ensure that no more than 20% of those surveyed, who are 51 or older, live in a state bordering on Mexico.
MSA decides that all surveys should be conducted in person. It estimates that the costs of reaching people in each age group and region category will vary because of travel costs, limited access hours, etc. Based on previous surveys, MSA has estimated these costs as outlined below.
COST PER PERSON SURVEYED ($)
AGE
REGION Under 30 31 - 50 Over 50
State Bordering Mexico 7.50 6.80 5.50
State NOT Bordering Mexico 6.90 7.25 6.10
MSA’s goal is to meet the five sampling requirements at the least possible cost. Formulate an appropriate mathematical problem, which, when solved, will provide the number of households in each age/region group to be surveyed, while meeting the five listed requirements at minimum total cost. (You do not need to solve the model.) Clearly define your objective and your variables.
Answer
Objective: To minimize the cost of the study while achieving the requirements set forth.
Decision Variable: The number of respondents from each age group in a state bordering Mexico or not bordering Mexico
Under 30=Y
31-50=M
Over 50=O
Bordering Mexico=B
Not Bordering Mexico=NB
X11 = number of respondents Y from B X12 = number of respondents M from B X13 = number of respondents O from B
X21 = number of respondents Y from NB X22 = number of respondents M from NB X23 = number of respondents O from NB
Subject To:
Total respondents are ? 2300
X11+ X12+ X13+ X21+ X22+ X23?2300
Total respondents Y are ? 1000
X11+ X21?1000
Total respondents M are?600
X12+ X22?600
Total respondents B is? 15% of2300
X11+ X12+ X13?2300(.15)
Total respondents NB is? 20% of O
This is what I have so far. Did I miss the mark? Do I need to add anything?