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A market research firm has been retained to conduct focus group interviews for a real estate company. Plans are made to classify participants to age: over 45 or 45 and under and as to whether or not they have recently bought and/or sold a house (within the last two years). Specific guidelines have been developed:
• At least 100 people must be selected• At least 75% of the participants must have bought or sold a house recently• Of those who have not bought or sold recently, at least 40% must be over 45 years of age• No more than 40% of participants should be 45 or under
There are preliminary screenings with associated costs. The cost for each participant begins at $10. Additional contact with those over 45 raises the cost by $12. Additional time with the recent buyers and sellers adds $7 to the cost of including those participants. Formulate a linear integer programming model to determine the amount of and type of participants that minimizes total cost. Use integer programming to establish whole numbers for the solution variables.
The decision variables, Need a physical explanation as to why X37 = 400, X78 = 0, and X48 = 400. I need for these computer generated numbers to make sense and be able to justify them
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