Problem 2: The map of five counties and their population in thousands are shown.

Question

Problem 2: The map of five counties and their population in thousands are shown. The federal agency of the CDC (Centers for Disease Control and Prevention) is planning to fund two adjacent counties in this area to offer mass vaccination clinics to the public. For example counties A and B can join together to offer a CDC funded mass vaccination clinic to their population of 80K people, but counties A and E or A and D cannot, as they are not neighbors. Formulate an IP that identifies two pairs of adjacent counties with maximum combined people. o adjacent A.25 B,55 c,15 D,45

Explanation / Answer

Maximise 25Xa+55Xb+15Xc+45Xd+35Xe

subject to

Xa+Xb = 2

Xa+Xc = 2

Xb+Xc = 2

Xc+Xe = 2

Xb+Xe = 2

Xb+Xd = 2

Xd+Xe = 2

Xa+Xd = 0

Xa+Xe = 0

Xc+Xd = 0

Where ?Xa XbXcXdXe {o,1}

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