Question 2 (10 marks)

With the urgency of trying to get so many individuals vaccinated against the Covid-19 virus, it is important to be able to offer clinics in places where most individuals can and want to be able to access clinics in their neighbourhoods. Unfortunately, costs of setting up clinics and running them are somewhat expensive. The county health unit in one particular county in Ontario is not only responsible for setting up and running these clinics, it is also responsible for any expenses involved with these clinics. The health unit in this county has identified 8 potential locations, the neighbourhoods (labelled 1 through 10) in the county that each location is most likely to attract potential individuals to get their vaccinations, and, the estimated total costs of setting up and running the clinics in each of these potential locations until the clinics are no longer needed there.

The following table includes the potential locations (labelled A through H), the neighbourhoods in the county where each which location is likely to attract individuals and the estimate costs associated with these potential locations. Using A, B, , H as the symbols for the decision variables, and, the information associated with each potential location, formulate the following that will allow the health unit to determine where to locate the clinics so that all individuals in the county will be attracted to at least one of the chosen clinics at minimum cost.

Potential location Neighbourhoods Covered Cost ($)

A 1, 4, 7 12,000

B 1, 5, 9, 10 17,000

C 2, 3, 9 8,000

D 4, 8 7,500

E 1, 6 6,000

F 5, 7, 8 8,700

G 4 4,500

H 2, 6 5,800

1. The objective function (You can just enter the first 2 entries and the last 2 entries using ,,, in between the first 2 and last 2 entries)

2. The basic constraint for neighbourhood 4

3. If location C is chosen, location B cannot be chosen

4. If locations A or F are chosen, location E must be chosen

5. Both D and H must be selected or neither can be selected

6. Location G can only be selected if locations A and D are selected

7. At least 2 locations which cost no more than $8,000 each must be selected