A national commission is deciding which military bases to close in order to save at least $85 million per year. The table that follows shows projected annual savings (millions of dollars) for each of five possible closings, together with the implied percent loss of military readiness and the number of civilian workers (thousands) who would lose their jobs.

Base 1 2 3 4 5 Savings 24 29 45 34 80 Readiness 1.0 0.4 1.4 1.8 2.0 Workers 2.5 5.4 4.6 4.2 14.4 Each base must be left open or completely closed, and the commission wants to meet the required savings while minimizing both readiness loss and unemployment.

(a) Briefly explain how this base-closing problem can be modeled by the multiobjective ILP min 1.0x1 + 0.4x2 + 1.4x3

+ 1.8x4 + 2.0x5 min 2.5x1 + 5.4x2 + 4.6x3

+ 4.2x4 + 14.4x5 s.t. 24x1 + 29x2 + 45x3

- 34x4 + 80x5 Ú 85 xt = 0 or 1, j = 1,c, 5

(b) and

(c) as in Exercise 8-1.