Your team is tasked with the planning of the transportation of vaccine from the manufacturers to the vaccination clinics, all of which are in Virginia. The table below provides the locations of the manufacturing facilities and the vaccination clinics in addition to the production capacities and the vaccine demand. However, you can only choose three of them.

a.(10 pts.) Calculate the distance matrix which contains the distances from each location to the others. You can make reasonable assumptions and use any tools. Concisely explain your method.

b.(10 pts.) Model the problem.

c.(15pts.) Provide a transportation plan which minimizes the total distance travelled and clearly contains the choice of manufacturing facilities, the number of vaccine shots to be transported, and the source/destination for them

d.(5 pts.) Provide a figure which represents your proposed solution visually.

Potential Manufacturing Facilities Vaccination Clinics No. Location Vaccine Production Capacity No. Location Demand 1 Norfolk 25000 1 Virginia Beach 17000 2 Suffolk 10000 2 Alexandria 10000 3 Richmond 15000 3 Blacksburg 7000 4 Hampton 12000 4 Charlottesville 6500 5 Lynchburg 17000 5 Lake Ridge 4500 6 Manassas 30000 7 Arlington 15000 8 Newsport News 18000 9 Dale City 21000 10 Reston 16000