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Ballplayer Selection using linear progression (LP)

The Dubuque Sackers, a class D baseball team, face a tough four-game road trip against league rivals in Des Moines, Davenport, Omaha, and Peoria. Manager "Red" faces the task of scheduling his four starting pitchers for appropriate games. Because the games are to be played back to back in less than one week, Revelle cannot count on any pitcher to start in more than one game. Revelle knows the strengths and weaknesses not only of his pitchers, but also of his opponents. He has developed a performance rating for each of his starting pitchers against each of these teams. The ratings are:
Starting Pitcher: Des Moines Davenport Omaha Peoria
Dead-Arm Jones 0.60 0.80 0.50 0.40
Spitball Baker 0.70 0.40 0.80 0.30
Ace Parker 0.90 0.80 0.70 0.80
Gutter Wilson 0.50 0.30 0.40 0.20

What pitching rotation should manager Revelle set to provide the highest total of the performance ratings?

a) Formulate this problem using LP.
b) Solve the problem.

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Solution Summary

Solution is a PDF of the LP model and the solution using Excel Solver.