Question 1 Parenz-Care is a budding business enterprise specialising in childcare and growth. It has a website with interesting information and advice on nutrition for children, safety, health supplements, health and recreation for children, parenting tips and children's education Since its establishment three years ago, Parenc-Care has garnered quite a following among young parents. The Q & A section in its website is especially popular with parents posting questions varying from nutrition for children to ways to handle hyperactive kids and educational concerns in Singapore's stressful school environment. Recently Parerc-Care has engaged your market research firm to help conduct a telephone interview exercise. It is interested to solicit views from its customer base as well as from the public. The survey feedbacks will be used to improve its products and services, particularly in the areas of child nutrition, parenting skills and upcoming tuition services. Three family types have been identified for the interviews, viz: i One-child family ii. Two-child family 111. Three-child family The interview questionnaire for each family type is not the same in contents although there are some core questions asked for each family type. The contents for the three-child family questionnaire are more complex and comprehensive which requires more time and hence cost) to conduct compared with the other two questionnaires Parerc-Care's request for your firm's services comprises the following requirements: The telephone surveys will be conducted over a period of 3 months (1) Both Morning-interviews (9am to 12.00 noon) and Evening-interviews (6pm to 9.00pm) are to be conducted on weekdays while interviews on Saturdays are limited to mornings only (9am to 12.00 noon). (2) An interview is deemed completed only if the questionnaire involved is completed. (3) The total number of households for the entire survey exercise must be at least 2200. (4) The cost per interview for the different family types is given in the table below: Saturdays Family Type One-Child Two-child Three-child Weekdays Morning Evening $20 S22 S23 S25 S26 S28 Table 1: Unit cost per Interview S20 $23 $26 (5) The total number of respondents in weekday Evening-interviews must be at least equal to the total number of respondents in weekday Morning-interviews. 6 The minimum number of Weekday Interviews per family type must comply with the requirements in Table 2 below. No such requirement applies to Saturday interviews. However, the combined total of two-child and three-child household interviews on Saturdays must be at least 110, Minimum number of Weekday Interviews per Family Type One-Child Two child Three-child 650 600 700 Table2. Minimum Number of Weekday Interviews Parenc-Care also has a special requirement on the allocation ratio (in percentages) of weekday Evening-interviews to weekday Morning-interviews per family type. These are specified in table 3 below: Ratio of Type of Household Evening to Morning Intensions for Weekdays One-Child 55.45 Two-child 60:40 Three-child 60:40 Table3 Interview Allocation Ratios For example, for two child households, if a total of 100 Morning-interviews on weekdays is to be conducted, 150 Evening-interviews must also be conducted to comply with the stated ratio. (a) Based on the above information, develop a Lincar Programming model comprising algebraic equations and appropriate inequalities to minimise the cost of the entire interview exercise (LP model: 22 marks) (b) Identify three (3) practical assumptions that support the validity of your Linear Programming model Solve the Linear Programming model by using the Excel Solver and present your Answer and Sensitivity Reports as generated by the Excel Solver software (you are not permitted to present these reports in your own format) (Answer Report: 3 marks, Sensitivity Report: 3 marks) Questions 1(d) and (e) must be solved without the aid of the Excel Solver. Show all calculations clearly (d) A week before the interview exercise commences, Parenz-Care requested for two changes to the following cost of interviews, viz: (i) Morning-interviews for two-child households to be reduced by $2 (ii) Evening-interviews for Three-child households to be reduced by $2. If your firm agrees to the cost reductions requested by Parenz-Care, interpret if these changes will impact the optimal cost found earlier? Illustrate the principles or concepts used to determine your answers. (Calculations: 6 marks; Explanations: 3 marks) (e) Parenz-Care also requested for a reduction of 80 interviews to be conducted for three- child households on Weekdays. Discuss if there will be any change to the optimal cost of the telephone survey exercise