a) Formulate and implement the mathematical model to solve this problem b) How much will it cost for the plan?
The centre has four floors with five rooms. Rooms 1-3 are for children under the age of 3. Room 4 is mainly for children at the age of 3 but this room has some 4-year-old children mixed in due to a transition to a kindergarten Room 5 is mainly for children at the age of 4. However, some 5-year-old children still attend because they are waiting for a term to open in a kindergarten. According to the Assistant Coordinator, the current numbers of children attending each day in each room and the maximum room capacities are summarised in the table below: Room 1 Room 2 Room 3 Room 4 Room 5 16 3-4 12 Max Capacity Age Monday Tuesday Wednesday Thursday Friday 10 10 13 12 According to the National Quality Framework (NQF), the minimum ratio of educators to children is 1:4 for 0-35 months and 1:11 for 36+ months. Although the NOF ratios are calculated across the service, and not by individual rooms, for practical and safety the centre calculates the ratio on a room-by-room basis. Generally, there are two levels of qualifications required to work as educators: Certificate III and Diploma. To comply with the NQF and to offer high quality care, in each room, the centre quires one educator must have a Diploma qualification for every three educators. For example, if Room 1 requires 3 educators, one of them must have a Diploma and the other two may have either a Diploma or a Certificate Ill qualification. However, if Room 1 requires 4 educators, two of them must have a Diploma qualification. The centre has 16 permanent educators which are summarised in the table below: Educator Qualification Available Time Available Day 1 Diploma 09:30-18.00 Mon-Fri 2 Certificate III 09:00-16:30 Mon-Fri 3 Certificate III 10:00-17:30 Mon-Fri Diploma 07:30-16:00 Mon-Thu 5 Certificate III 10:00-17:30 Mon-Fri 6 Diploma 07:30-16:00 Mon-Fri 7 8 9 10 11 12 13 14 15 16 Diploma Certificate III Certificate III Diploma Diploma Certificate III Certificate III Diploma Diploma Certificate III 09:30-18.00 10:00-17:30 09:00-16:30 07:30-16.00 09:30-18.00 09:30-16:30 09.00-17:30 07:30-16:00 09:30-18:00 09:30-17:00 Mon-Fri Mon-Fri Mon-Fri Tue-Fri Mon-Fri Mon-Fri Mon-Fri Mon-Fri Tue-Fri Mon-Fri In addition, the centre has a contract with the agency. If the centre requires additional qualified educators, either Certificate ill or Diploma, they can contact the agency for an arrangement. The agency educators are paid only when needed, and there is no on-going cost required. Currently, the centre has booked eight educators on standby through the agency. The centre pays the wages to the permanent educators according to the Children's Services Award 2010. The wages depend on the experience and qualifications of the educators which are summarised below: Level Experience 3.1 On commencement 3.2 After 1 year 3.3 After 2 years 4.1 On commencement 4.2 After 1 year 4.3 After 2 years Hourly Rate $22.70 $23.48 $24.22 $26.74 $27.14 $27.55 Level-3 employees are Certificate-Ill qualified educators, and Level-4 employees are Diploma qualified educators. All permanent educators in this centre have more than two years of experience working in this industry. The hourly wage to hire an agency educator, whether Certificate Ill or Diploma, is $51.77; and they will work for 8 hours. Since one of the duties of educators is to engage and familiar with children, when they are assigned to supervise one room, they wil stay in the same room for the whole week. The Centre Manager, Joan Gilmore, wants to create a roster for the educators with a minimum cost plan. She wants the plan that (1) each permanent educator will be given a job to do and (2) in case that there are not sufficient educators, an agency educator will be given a job: The centre has four floors with five rooms. Rooms 1-3 are for children under the age of 3. Room 4 is mainly for children at the age of 3 but this room has some 4-year-old children mixed in due to a transition to a kindergarten Room 5 is mainly for children at the age of 4. However, some 5-year-old children still attend because they are waiting for a term to open in a kindergarten. According to the Assistant Coordinator, the current numbers of children attending each day in each room and the maximum room capacities are summarised in the table below: Room 1 Room 2 Room 3 Room 4 Room 5 16 3-4 12 Max Capacity Age Monday Tuesday Wednesday Thursday Friday 10 10 13 12 According to the National Quality Framework (NQF), the minimum ratio of educators to children is 1:4 for 0-35 months and 1:11 for 36+ months. Although the NOF ratios are calculated across the service, and not by individual rooms, for practical and safety the centre calculates the ratio on a room-by-room basis. Generally, there are two levels of qualifications required to work as educators: Certificate III and Diploma. To comply with the NQF and to offer high quality care, in each room, the centre quires one educator must have a Diploma qualification for every three educators. For example, if Room 1 requires 3 educators, one of them must have a Diploma and the other two may have either a Diploma or a Certificate Ill qualification. However, if Room 1 requires 4 educators, two of them must have a Diploma qualification. The centre has 16 permanent educators which are summarised in the table below: Educator Qualification Available Time Available Day 1 Diploma 09:30-18.00 Mon-Fri 2 Certificate III 09:00-16:30 Mon-Fri 3 Certificate III 10:00-17:30 Mon-Fri Diploma 07:30-16:00 Mon-Thu 5 Certificate III 10:00-17:30 Mon-Fri 6 Diploma 07:30-16:00 Mon-Fri 7 8 9 10 11 12 13 14 15 16 Diploma Certificate III Certificate III Diploma Diploma Certificate III Certificate III Diploma Diploma Certificate III 09:30-18.00 10:00-17:30 09:00-16:30 07:30-16.00 09:30-18.00 09:30-16:30 09.00-17:30 07:30-16:00 09:30-18:00 09:30-17:00 Mon-Fri Mon-Fri Mon-Fri Tue-Fri Mon-Fri Mon-Fri Mon-Fri Mon-Fri Tue-Fri Mon-Fri In addition, the centre has a contract with the agency. If the centre requires additional qualified educators, either Certificate ill or Diploma, they can contact the agency for an arrangement. The agency educators are paid only when needed, and there is no on-going cost required. Currently, the centre has booked eight educators on standby through the agency. The centre pays the wages to the permanent educators according to the Children's Services Award 2010. The wages depend on the experience and qualifications of the educators which are summarised below: Level Experience 3.1 On commencement 3.2 After 1 year 3.3 After 2 years 4.1 On commencement 4.2 After 1 year 4.3 After 2 years Hourly Rate $22.70 $23.48 $24.22 $26.74 $27.14 $27.55 Level-3 employees are Certificate-Ill qualified educators, and Level-4 employees are Diploma qualified educators. All permanent educators in this centre have more than two years of experience working in this industry. The hourly wage to hire an agency educator, whether Certificate Ill or Diploma, is $51.77; and they will work for 8 hours. Since one of the duties of educators is to engage and familiar with children, when they are assigned to supervise one room, they wil stay in the same room for the whole week. The Centre Manager, Joan Gilmore, wants to create a roster for the educators with a minimum cost plan. She wants the plan that (1) each permanent educator will be given a job to do and (2) in case that there are not sufficient educators, an agency educator will be given a job
