SOLVE USING SOLVER AND SIMPLE LP (STEP BY STEP)

51. Based on Machol (1970). A swimming coach is putting together a relay team for the 400- meter relay. Each swimmer must swim 100 meters of breaststroke, backstroke, butterfly, or freestyle, and each swimmer can swim only one race. The coach believes that each swimmer can attain the times given in the file P05_51.xlsx. To minimize the team's total time for the race, which swimmers should swim which strokes? Index Problem 5.51. Assigning Swimmers to Events (p. 269) Indexing locations Swimmer Index Style Hall 1 Free Spitz 2 Breast Montgomery 3 Butterfly Jastremski 4 Back 1 2 3 4 Flows = Flow balance constraints Swimmer Flow out 1 2 3 4 1 1 1 1 Flow in Swimmer 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 Style 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Time 54 54 51 53 51 57 52 52 50 53 54 56 56 54 55 53 = Style 1 2 3 4 1 1 1 1 4 Total time