Question

Chapter 6 Problem 12 number of new 12. Health Care Systems of Florida (HCSF) is planning to build a emergency-care clinics in central Florida. HCSF management has divided a map of the area into seven regions. They want to locate the emergency centers so that all seven regions will be conveniently served by at least one facility. Five possible sites are available for constructing the new facilities. The regions that can be served conveniently by each site are indicated by X in the following table: Possible Building Sites Apopka Sanford Casselberry Maitland Region Altamonte X 1 X 2 X X 3 X X 4 X X 5 X X 6 X X 7 X X Cost ($1,000s) $450 $650 $550 $500 $525 What is the optimal solution?

Answer 1

A C E 1 means that region would be served. O means not served Casselberry 2 Sanford Altamonte Apopka Maitland Region 3 1 1 1 4 1 1 1 2 1 0 5 3 1 1 0 C 4 0 1 1 7 1 0 8 1 6 0 C 1 9 7 1 0 0 0 1 550000 525000 10 Cost 450000 650000 500000 11 Decision Variables 12 Whether to select a site or not. 1 means selected.O means not selected Casselberry 13 Sanford Altamonte Apopka Maitland 14 Yes/No 15 Objective function 16 Minimize total cost 17 SUMPRODUCT(B14:F14,B10:F10) Constraints 18 19SUMPRODUCT(SB$14:$F$14,B3:F3) 20 SUMPRODUCT(SB$14:SF$14,B4:F4) 21 SUMPRODUCT($ B$14:$ F$14,B5: F5) 22 SUMPRODUCT($ B$14:$ F$14,B6:F6) 23 SUMPRODUCT($ B$14:$ F$ 14,B7:F7) 24 SUMPRODUCT($ B$14:$ F$ 14,B8:F8) 25 SUMPRODUCT(SB$14:$F$14,B9:F9) 1 1 1 1 1 1 1 co

A C D E F G 1 means that region would be served. O means not served Altamonte Apopka Casselberry Maitland 2 Sanford Region 3 1 1 0 1 4 2 1 1 0 1 1 5 3 C 1 0 1 6 1 4 0 0 7 1 1 0 0 8 6 0 1 1 7 C 0 0 1 1 10 Cost 450000 650000 550000 500000 525000 11 Decision Variables 12 Whether to select a site or not. 1 means selected. O means not selected Altamonte Apopka Casselberry Maitland 13 Sanford 14 Yes/No 15 Objective function 16 Minimize total cost 17 18 Constraints 19 C 1 20 C 1 21 1 22 1 23 C 1 24 C 1 25 1 OOO OO O st

Solver Parameters rf SAS17 Set Objective: To: 0 O Min Value Of Max By Changing Variable Cells: SB$14:SFS14 Subject to the Constraints: SAS19:SA$25 SB$14:SFS14 binary SCS19:SCS25 >= Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear, Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth Help Solve Close X

A C F G Decision Variables 11 Whether to select a site or not. 1 means selected. 0 means not selected 12 Sanford Altamonte Apopka Casselberry Maitland 13 Yes/No 14 1 0 0 1 1 Objective function 15 Minimize total cost 16 17 1475000 Constraints 18 19 1 1 20 3 1 21 1 1 22 1 1 23 1 1 24 1 1 25 2 1 26 27 28 29