This Course related to Quantitative Methods in Engineering Management.Please solve it step by step to understand it$.$Thank youProblem $3.$ A director in the police department is responsible for assigning policemen to three

police stations in one region. He recognizes the varying distance between where policemen live

and the three police stations. The director recognize that all the policemen live in five

neighborhoods $(1,2,3,4,5.$ He attempts to establish a plan that will minimize the total number

of miles traveled by all policemen. He also recognizes that if a policeman happens to live in a

certain neighborhood and is assigned to a police station in that neighborhood, then his$/$her travel

millage will be considered insignificant. The three police stations are located in neighborhoods $2,$

$3,$ and $5.$ Each police station has a different minimum demand for policemen. A policeman cannot

travel more than $10$ KM $.$ All available policemen must be assigned. The following table shows the

number of policemen living in each neighborhood and the driving distance in miles from between

neighborhoods:

Q$1.$ Set up the objective function and constraints of this problem using LP so that the total miles

traveled by all policemen is minimized. $(15$ pts $)$

Q$2.$ Solve the problem and provide the optimal solution. $(10$pts$)$

Q$3.$ How should the director further minimize the total miles traveled assuming he can reduce one

of the requirements? $(5$pts$)$