After hurricane Sandy county governments has been order to d

After hurricane Sandy, county governments has been order to develop disaster plans for assigning casualties to hospitals in the event of another serious weather event.

Hospital

(travel times—minutes)

Town

Point Pleasant

Atlantic

Estimated Casualties

Margate

10

15

250

Ventnor

20

5

350

Longport

15

20

200

Capacity

300

500

The estimated casualties from the three towns, their average travel times to the two hospitals and the capacity of each hospital is listed in the table above.

Formulate a linear program to assign casualties to the hospital so as to minimize travel time, take care of the estimated casualties given the capacity of the hospitals.

Solve this problem using Excel’s Solver. What is the optimal solution? Which constraints are binding? Non-binding?

Solution

The total amount of time lost to transport will thus be

T = 10*x1+ 15 *y1 + 20*x2 +5*y2+ 15*x3 +20*y3

and we have to minimize it.

we know by capacity

x1+x2+x3 <=300

y1+y2+y3 <=500

and x1, x2, x3 , y1, y2, y3 are non negative.

x1 + y1 = 250

x2 +y2 =350

x3 + y3 =200

By solving it

Optimal solution

T= 8000;

x1= 100,

y1= 150,

x2= 0,

y2= 350,

x3= 200,

y3= 0