Northwest General Hospital Northwest General, a large hospital in Providence, Rhode Island, has initiated a new procedure to ensure that patients receive their meals while the food is still as hot as possible. The hospital will continue to prepare the food in its kitchen, but will now deliver it in bulk (not individual servings) to one of three new serving stations in the building. From there, the food will be reheated, meals will be placed on individual trays, loaded onto a cart, and distributed to the various floors and wings of the hospital. The three new serving stations are as efficiently located as possible to reach the various hallways in the hospital. The numbers of trays that each station can serve are shown below: Location Capacity (Meals) Station 5A= 200, Station 3G= 225, Station 1S= 275. There are six wings in Northwest General that must be served. The number of patients in each wing is as follows: Wing Patients 1- 80, 2- 120, 3- 150, 4- 210, 5- 60, 6- 80. The purpose of the new procedure is to increase the temperature of the hot meals that the patient receives. Therefore, the amount of time needed to deliver a tray from a serving station will determine the proper distribution of food from serving station to wing. The table below summarizes the time associated with each possible distribution channel. Distribution Time (Minutes) From/To Wing 1 Wing 2 Wing 3 Wing 4 Wing 5 Wing 6, Station 5A- 12 11 8 9 6 6, Station 3G- 6 12 7 7 5 8, Station 1S- 8 9 6 6 7 9.
Formulate and solve a linear program to determine how best to distribute the meals.