There are five hospitals in Brooklyn that will be served by a blood bank. Their locations and

monthly demand $($in terms of deliveries per month$)$ are given in the table in the Excel file. Suppose

the cost of opening a new blood bank facility is $$1$ million. Once built, a facility will last for

roughly $10$ years. Further, delivery cost is $$1/$unit distance traveled$/$trip$,$ and rectilinear distance

is used. There are three possible locations for blood banks $(4,11),(3,6),(12,5)$ and a blood

bank can make $450$ deliveries per month at most. We wish to determine which locations to choose

that minimizes the total cost. In order to define fixed and variable costs in the same terms, we need

to compute the monthly payment for the facility over the $10-$year life. If an annual discount rate

of $8\%$ is used, then the monthly payment per facility is PMT $(8\%/12,12*10,1000000)=$ $$12,133.$

$($a$)$ Develop an optimization model to select blood bank location to meet the demands among five

hospitals. Use the Manhattan distance metric.

$($b$)$ Solve the model using the Gurobi Python Interface, and discuss your results