In the event of a disaster situation at State University from weather, an accident, or terrorism, victims

Question:

In the event of a disaster situation at State University from weather, an accident, or terrorism, victims will be transported by emergency vehicles to three area hospitals: County General, Memorial, and All Souls. County General is (on average) 10 minutes away from State, Memorial is 20 minutes away, and All Souls is 35 minutes away. State wants to analyze a hypothetical disaster situation in which there are 15 victims with different types of injuries. The emergency facilities at County General can accommodate, at most, 8 victims; Memorial can handle 10 victims; and All Souls can admit 7 victims. A priority has been assigned for each victim according to the hospital that would best treat that victim€™s type of injury, as shown in the following table (where 1 reflects the best treatment).

For example, for victim 1€™s type of injury, the best hospital is County General, the next best is Memorial, and All Souls is third best.
a. Formulate and solve a linear programming model that will send the victims to the hospital best suited to administer to their specific injuries while keeping the average transport time to 22 minutes or less.
b. Formulate and solve a linear programming model that will minimize the average transport time for victims while achieving an average hospital priority of at least1.50.