Based on the above information, develop a Linear Programming model comprising algebraic equations and appropriate inequalities to minimise the cost of the entire interview exercise.
SECTION II 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, Parenz-Care has gamered 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 Parenz-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: One-child family Two-child family iii 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. Parenz-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:Family Type Weekdays Saturdays Morning Evening One-Child $20 $22 $20 Two-child $23 $25 $23 Three-child $26 $28 $26 Table 1: Unit cost per Interview (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 I wo-child Three-child 650 600 700 Table2: Minimum Number of Weekday Interviews Parenz-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: Type of Household Ratio of Evening to Morning Interviews 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
