Question

Market Survey, Inc. (MSI), specializes in evaluating consumer reactions to new products, services, and advertising campaigns. A client firm has requested MSI's assistance in ascertaining consumer reaction to a recently marketed household product. During meetings with the client, MSI agreed to conduct door- to- door personal interviews to obtain responses from households with children and households without children. In addition, MSI agreed to conduct both day and evening interviews. Specifically, the client's contract called for MSI to conduct 1000 interviews under the following quota guidelines: 1. Interview at least 400 households with children 2. Interview at least 400 households without children 3. The total number of households interviewed during the evening must be greater than or equal the number of households interviewed during the day 4. At least 40 percent of the interviews for households with children must be conducted during the evening 5. At least 60 percent of the interviews for households without children must be conducted during the evening Because the interviews for the households with children take additional interviewer time and because evening interviewers are paid more than day time interviewers, the cost varies with the type of interview. Based on previous research studies, estimate of the interview costs are as follows: Household Children No Children Interview Cost Day $20 $18 Evening Formulate and solve a linear programming model that will answer the following question What is the household and the time of the day interview plan that will satisfy the contract requirements at a minimum total interviewing cost? Make sure to.. 1. A complete algebraic formulation model for the Market Survey case. 2. Your Excel solution along with all the reports generated through Excel. 3. Your own written report that explains your findings.

Answer 1

Part 1:

Decision Variable

HCD = no. of interviews of household with children in day time

HCE = no. of interviews of household with children in evening time

HND = no. of interviews of household without children in day time

HNE = no. of interviews of household without children in evening time

Objective Function:

Objective function of the problem is to minimize the total cost of interviews:

Cost = cost per interview x no. of interviews

Minimize Z = $20HCD + $25HCE + $18HND + $20HNE

Subject to:

Sr. No.	Constraint	Equation
1	Total 1000 interviews are to be conduct	HCD + HCE + HND + HNE = 1000
2	Interview at least 400 households with children	HCD + HCE >= 400
3	Interview at least 400 households without children	HND + HNE >= 400
4	Total evening interviews >= total day interviews	HCE + HNE >= HCD + HND - HCD + HCE - HND + HNE >= 0
5	At least 40% of the interviews for household with children must be conducted during evening	HCE >= 0.4(HCD + HCE) -0.4HCD + 0.6HCE >= 0
6	At least 60% of the interviews for household without children must be conducted during evening	HNE >= 0.6(HND + HNE) -0.6HND + 0.4HNE >= 0
7	Non-negativity constraint	HCD, HCE, HND, HNE >= 0

Part 2:

Excel Model:

$FS10 4096 HC must be in evening LHS 22

Optimal Solution:

No. of interviews of Household with children in day time = 150

No. of interviews of Household with children in evening time = 250

No. of interviews of Household without children in day time = 171.4

No. of interviews of Household without children in evening time = 428.6

Total Cost = $20,907.14

Reports: