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Question
NARRBEGIN: SA_76_82A marketing research professor is conducting a telephone survey and needs to contact at least 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 to make a daytime call and $4 (because of higher labor costs) to make an evening call. The table shown below lists the expected results. For example, 10% of all daytime calls are answered by a single male, and 15% of all evening calls are answered by a single female. Because of a limited staff, at most half of all phone calls can be evening calls. Determine how to minimize the cost of completing the survey.
| Percentages | Daytime | Evening |
| Wife | 25% | 25% |
| Husband | 15% | 30% |
| Single male | 10% | 25% |
| Single female | 15% | 15% |
| None | 35% | 5% |
(A) What is the objective function in this problem?
(B) What are the constraints in this problem? Write an algebraic expression for each.
(C) Find an optimal solution to the problem using the formulation given in (A) and (B). What is the call plan, and what is the total cost?
(D) Implement the model in (C) in Excel Solver and obtain an answer report. Which constraints are binding on the optimal solution?
(E) Obtain a sensitivity report for the model in (D). If the professor could cut the cost of evening calls from $4 to $3, what would the new calling plan be?
(F) Again using the sensitivity report obtained for (E), suppose the professor could get by with just 100 calls for single females. What would the call costs be in that case? Explain your answer.
Answer
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