A rise in COVID infections strains the resources of health care facilities. Respirators are critical resources that might be in shortage due to high demand. In an attempt to manage their critical resources, a group of hospitals within the Beirut municipality decided to pool their resources to satisfy the demand for respirators. Each hospital reports the number of respirators at its disposal. At the end of each week, the hospital management boards (HMBs) provide an updated estimate on the projected demand for respirators at each hospital and determines whether any of the respirators needs to be reassigned. There is a transportation cost associated with reassigning a respirator to a different hospital. Therefore, the HMBs need to determine a minimum cost assignment of respirators to hospitals that satisfies the next weeks projected demand at each hospital. As an example, consider five hospitals with five locations within the Beirut municipality. The HMB evaluates the need to relocate respirators based on the monthly projected demand for each hospital. The cost of reassigning a respirator from hospital i to hospital j is 100,000 LBP per kilometer of travel of distance for hospital i to hospital j. An extra setup cost (due to overhead costs) of 200,000 LBP is incurred for each order from hospital i to j. For each of the hospitals locations, the table below lists the X and Y coordinates of the hospital, the number of respirators currently assigned, and the projected demand for next period.What is the optimal cost and decision? Extra Credit: Formulate an Integer Linear Program for the case with H hospitals where rh is the number of respirators at hospital h, and dh is the projected demand for hospital h (for h = 1,2, H). Denote the coordinates of hospital h by Xh and Yh.

X-Coordinate (km) Y-Coordinate (km) Respirators at Hospital Projected Demand for next Week Hospital 1 36 20 30 35 Hospital 2 23 30 10 15 Hospital 3 23 56 15 10 Hospital 4 10 15 15 20 Hospital 5 5 5 20 10 X-Coordinate (km) Y-Coordinate (km) Respirators at Hospital Projected Demand for next Week Hospital 1 36 20 30 35 Hospital 2 23 30 10 15 Hospital 3 23 56 15 10 Hospital 4 10 15 15 20 Hospital 5 5 5 20 10