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Formulate a linear programming problem that can be used to solve the following question. An airline has three types of airplanes and has contracted with a tour group to provide transportation for a minimum of 72 first-class, 56 tourist, and 112 economy-class passengers. The first plane costs $3800 for the trip and can accommodate 48 first-class, 10 tourist, and 28 economy-class passengers; the second plane costs $4500 for the trip and can accommodate 14 first-class, 14 tourist, and 42 economy-class passengers; the third plane costs $6000 for the trip and can accommodate 28 first-class, 30 tourist, and 10 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? x = number of first type of airplane v y = number of second type of airplane z = number of third type of airplane Minimize vy F = (objective function) Subject to (first-class passengers) (tourist passengers) (economy-class passengers) x 0, y3 x 0, zE |x 0 (nonnegativity constraint) Additional Materials m.n..

Formulate a linear programming problem that can be used to solve the following question. An airline has three types of airplanes and has contracted with a tour group to provide transportation for a minimum of 72 first-class, 56 tourist, and 112 economy-class passengers. The first plane costs $3800 for the trip and can accommodate 48 first-class, 10 tourist, and 28 economy-class passengers; the second plane costs $4500 for the trip and can accommodate 14 first-class, 14 tourist, and 42 economy-class passengers; the third plane costs $6000 for the trip and can accommodate 28 first-class, 30 tourist, and 10 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? x = number of first type of airplane v y = number of second type of airplane z = number of third type of airplane Minimize vy F = (objective function) Subject to (first-class passengers) (tourist passengers) (economy-class passengers) x 0, y3 x 0, zE |x 0 (nonnegativity constraint) Additional Materials m.n..

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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Formulate a linear programming problem that can be used to solve the following question. An airline has three types of airplanes and has contracted with a tour group to provide transportation for a minimum of 72 first-class, 56 tourist, and 112 economy-class passengers. The first plane costs $3800 for the trip and can accommodate 48 first-class, 10 tourist, and 28 economy-class passengers; the second plane costs $4500 for the trip and can accommodate 14 first-class, 14 tourist, and 42 economy-class passengers; the third plane costs $6000 for the trip and can accommodate 28 first-class, 30 tourist, and 10 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? x = | number of first type of airplane y = number of second type of airplane z = number of third type of airplane Minimize F = (objective function) Subject to (first-class passengers) (tourist passengers) (economy-class passengers) Vx 0, y S X 0, z = Vx 0 (nonnegativity constraint) Additional Materials еВook
Transcribed Image Text:Formulate a linear programming problem that can be used to solve the following question. An airline has three types of airplanes and has contracted with a tour group to provide transportation for a minimum of 72 first-class, 56 tourist, and 112 economy-class passengers. The first plane costs $3800 for the trip and can accommodate 48 first-class, 10 tourist, and 28 economy-class passengers; the second plane costs $4500 for the trip and can accommodate 14 first-class, 14 tourist, and 42 economy-class passengers; the third plane costs $6000 for the trip and can accommodate 28 first-class, 30 tourist, and 10 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? x = | number of first type of airplane y = number of second type of airplane z = number of third type of airplane Minimize F = (objective function) Subject to (first-class passengers) (tourist passengers) (economy-class passengers) Vx 0, y S X 0, z = Vx 0 (nonnegativity constraint) Additional Materials еВook
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