Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
Expert Solution & Answer
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Chapter 4, Problem 22RP

Explanation of Solution

Optimal solution:

  • Consider the preemptive programming problem of the Monroe Country of building a fire station.
  • This fire station covers four major towns that are mentioned in the given diagram:

  • The below given table specifies the average number of fire incidents in each of the towns:
TownLocationFire
1(10,20)20
2(60,20)30
3(40,30)40
4(80,60)25
  • Assume that (x,y) is the point where the fire station is build. Suppose a town with fire is located at point (a,b).
  • Depending upon the location of the fire station in town A, the value xa will be positive or negative. That is if (x,y) is in the east, then xa is positive, and therefore,
    • xa=ew
  • e and w are defined as non-negative. Hence, when xa is positive, xa=e and w=0. When xa is negative, xa=w and e=0.
  • Thus, the total distance between fire station and town is given by
    • d=e+w+n+s
  • Hence, the optimization equation is
  • Minimize z=20d1+30d2+40d3+25d4
  • The constraints for each town are
    • x10=e1w1
    • y20=s1n1
    • x60=e2w2
    • y20=s2n2
    • x40=e3w3
    • y30=s3n3
    • x80=e4w4
    • y60=s4n4
  • Thus the following LP formulation:
  • Minimize z=20d1+30d2+40d3+25d4
  • Subject to
    • x10=e1w1
    • y20=s1n1
    • x60=e2w2
    • y20=s2n2
    • x40=e3w3
    • y30=s3n3
    • x80=e4w4
    • y60=s4n4
    • d1=e1+w1+n1+s1
    • d2=e2+w2+n2+s2
    • d3=e3+w3+n3+s3
    • d4=e4+w4+n4+s4
  • The LP problem is solved using Lindo software

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Chapter 4 Solutions

Introduction to mathematical programming

Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
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