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# Statistics - Formulate as LP in a Spreadsheet and Solve

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A bank has \$650,000 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 10%, mortgages 8.5%, car loans 9.5%, and personal loans 12.5%. To make sure the portfolio is not too risky, the bank wants to restrict personal loans to no more than 25% of the total portfolio. The bank also wants to ensure that more money is invested in mortgages than in personal loans. And it wants to invest more in bonds than personal loans.

Formulate this as an LP in a spreadsheet and solve with Solver.
How much should the bank invest in each of the asset classes to maximize total expected return?

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#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.

\$2.19

## 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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