What is a projection?
2 answers:
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Answer:
a.
Look at the two attached figures please. The decision variables is the choice to build a fire station in which city.
So there are six decision variables each taking a value of either 0 or 1.
D1 = decision to build fire station in city 1, (1 denotes yes and 0 denotes no)
D2 = decision to build fire station in city 2, (1 denotes yes and 0 denotes no)
D3 = decision to build fire station in city 3, (1 denotes yes and 0 denotes no)
D4 = decision to build fire station in city 4, (1 denotes yes and 0 denotes no)
D5 = decision to build fire station in city 5, (1 denotes yes and 0 denotes no)
D6 = decision to build fire station in city 6, (1 denotes yes and 0 denotes no)
b.
Please look at attachment
C .
The figure 1 denotes the problem formulation in excel and shows all the formulas.
In first step, a matrix is prepared to denote all cities which are within 15 minutes by 1 and others by zero
A array of decision variables for selecting the city is shown. A 1 in cell implies that city is selected and 0 means the city is not selected.
A product of the selection variable and the value in the within 15 minutes matrix is calculated as shown by the formula.
The constraint is to ensure that all cities have at least one fire station mapped within 15 minutes.
d.
The problem is solved in Excel using integer programming and the solution is that City 2 and 4 should be selected for building fire stations and thus total no of fire stations are two with every city within 15 minutes.
Explanation:
