Problem 5 (20 points). To conduct a sociological survey, a research lab needs to reach at least 200 people aged 31-40, 150 people aged 41-50, 100 people aged 51-60, and 50 people aged 61-70. The survey is conducted by phone. The cost of making a daytime call and an evening call is $5 and $7, respectively. Based on historical data, it is expected that the ages of the respondents will be distributed as described in the following table. Age of the Respondent Percent of Daytime Calls Percent of Evening Calls 31-40 10 20 41-50 10 30 51-60 10 15 61-70 20 other 50 15 20 No more than 30% of all phone calls can be made in the evening. Formulate an LP minimizing the cost of conducting the survey while reaching the target number of respondents from each age group.

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Problem 5 (20 points). To conduct a sociological survey, a research lab needs to reach at least 200 people aged
31-40, 150 people aged 41-50, 100 people aged 51-60, and 50 people aged 61-70. The survey is conducted by
phone. The cost of making a daytime call and an evening call is $5 and $7, respectively. Based on historical
data, it is expected that the ages of the respondents will be distributed as described in the following table.
Age of the
Respondent
Percent of
Daytime Calls
Percent of
Evening Calls
31-40
10
20
41-50
10
30
51-60
10
15
61-70
20
other
50
15
20
No more than 30% of all phone calls can be made in the evening. Formulate an LP minimizing the cost of
conducting the survey while reaching the target number of respondents from each age group.
Transcribed Image Text:Problem 5 (20 points). To conduct a sociological survey, a research lab needs to reach at least 200 people aged 31-40, 150 people aged 41-50, 100 people aged 51-60, and 50 people aged 61-70. The survey is conducted by phone. The cost of making a daytime call and an evening call is $5 and $7, respectively. Based on historical data, it is expected that the ages of the respondents will be distributed as described in the following table. Age of the Respondent Percent of Daytime Calls Percent of Evening Calls 31-40 10 20 41-50 10 30 51-60 10 15 61-70 20 other 50 15 20 No more than 30% of all phone calls can be made in the evening. Formulate an LP minimizing the cost of conducting the survey while reaching the target number of respondents from each age group.
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