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, 9 14,000 B 1, 5, 9, 10 17,000 C 2, 3, 9 9,000 D 4, 8 7,500 E 1, 6, 10 6,000 F 5, 7, 8 8,700 G 4, 10 4,500 H 2, 6 5,800 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) The basic constraint for neighbourhood 10 If location C is chosen, location D must be chosen If locations A or H are chosen, location F must be chosen Both B and F must be selected or neither can be selected Location G can only be selected if locations B and C are selected
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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, 9 14,000
B 1, 5, 9, 10 17,000
C 2, 3, 9 9,000
D 4, 8 7,500
E 1, 6, 10 6,000
F 5, 7, 8 8,700
G 4, 10 4,500
H 2, 6 5,800
- 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)
- The basic constraint for neighbourhood 10
- If location C is chosen, location D must be chosen
- If locations A or H are chosen, location F must be chosen
- Both B and F must be selected or neither can be selected
- Location G can only be selected if locations B and C are selected
- At least 3 locations which cost no more than $10,000 each must be selected
Step by step
Solved in 3 steps
