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LP Scheduling problem

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A nursing home employs attendants who are needed around the clock. Each attendant is paid the same, regardless of when his or her shift begins. Each shift is 8 consecutive hours. Shift begin at 6 a.m., 10 am, 2 pm, 6 pm, 10 pm and 2 am. The following table shows the nursing home's requirements for the numbers of attendants to be on duty during specific time periods

a) what is the minimum number of attendants needed to satisfy the nursing home's requirements? b) The nursing home would like to use the same number of attendants determined in part (a) but would now like to minimize the total salary paid. Attendants are paid $16 per hour during 8am-8pm, and a 25% premium per hour during 8pm- 8am. How should the attendants now be scheduled?

SHIFT TIME NUMBER OF ATTENDANTS

A 2-6 A.M. 8
B 6-10 A.M. 27
C 10 A.M.-2 P.M. 12
D 2-6 p.M. 23
E 6-10 P.M. 29
F 10-2 A.M. 23

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This posting contains formulation and excel solver solution to the LP Staffing problem.

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Statistics: 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:
Opponent
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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