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Statistics - Formulate the LP model

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Thompson Distributors packages and distributes industrial supplies. A standard shipment can be packaged in one of 3 types of containers: A, K, T. A single class A container yields a profit of $9, a class K container yields a profit of $7 and a class T yields $15. Each shipment prepared requires a certain amount of packing material and a certain amount of time as shown in the table below. They have 130 pounds of packing material and 240 hours of packing time. Jason Thompson, head of the firm, must decide the optimal number of each class of container to pack each week. He is also boiund by the fact that he must also keep his 6 full-time packers employed all 240 hours each week. Formulate the LP model but do not solve.

Class of Container Packing Material (pounds) Packing Time (hours)
A 2 2
K 1 6
T 3 4

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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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