Scenario #2 (6 parts)- A marketing research professor is conducting a telephone
ID: 3326200 • Letter: S
Question
Scenario #2 (6 parts)- A 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).
(C.1) What is the call plan?
(C.2) 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? (You may put parts of the excel solver report here but you must explain here results in words)
(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? (You may put parts of the excel solver report here but you must explain the results in words)
(F) Again using the sensitivity report obtained for (E), suppose the professor could get by with just 100 calls for single females.
(F.1) What would the call costs be in that case?
(F.2) Explain your answer.
Scenario #2 (6 parts)- A 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%
Explanation / Answer
Let w1 and w2 are the number of daytime and evening calls are made to wives
Let h1 and h2 are the number of daytime and evening calls are made to husbands
Let m1 and m2 are the number of daytime and evening calls are made to single males
Let f1 and f2 are the number of daytime and evening calls are made to single females
Let n1 and n2 are the number of daytime and evening calls are made to none
Objective function is to minimize the cost
minimize Z = 2w1 + 2h1 + 2m1 + 2f1 + 2n1 + 4w2 + 4h2 + 4m2 + 4f2 + 4n2
Constraints are
1) At least 160 wives are to be contacted
0.25w1 + 0.25w2 >= 160
2) At least 140 husbands to be contacted
0.15h1 + 0.3h2 >= 140
3) At least 110 single adult males to be contacted
0.1m1 + 0.25m2 >= 110
4) At least 120 single adult females to be contacted
0.15f1 + 0.15f2 >= 120
5) At most half of all phone calls can be evening calls
w2 + h2 + m2 + f2 + n2 <= 0.5*(w1 + w2 + h1 + h2 + m1 + m2 + f1 + f2 + n1 + n2)
i.e. 0.5w2 - 0.5w1 + 0.5h2 - 0.5h1 + 0.5m2 - 0.5m1 + 0.5f2 - 0.5f1 + 0.5n2 - 0.5n1 <= 0
Hence LP formulation is
Min Z = 2w1 + 2h1 + 2m1 + 2f1 + 2n1 + 4w2 + 4h2 + 4m2 + 4f2 + 4n2
subject to,
0.25w1 + 0.25w2 >= 160
0.15h1 + 0.3h2 >= 140
0.1m1 + 0.25m2 >= 110
0.15f1 + 0.15f2 >= 120
0.5w2 - 0.5w1 + 0.5h2 - 0.5h1 + 0.5m2 - 0.5m1 + 0.5f2 - 0.5f1 + 0.5n2 - 0.5n1 <= 0
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