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 86 first-class, 50 tourist, and 116 economy-class passengers. The first plane costs $4400 for the trip and can accommodate 44 first-class, 16 tourist, and 22 economy-class passengers; the second plane costs $5400 for the trip and can accommodate 8 first-class, 16 tourist, and 42 economy-class passengers; the third plane costs $5800 for the trip and can accommodate 20 first-class, 28 tourist, and 12 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? x = number of first class passengers number of first type of airplane y = number of tourist class passengers number of second type of airplane z = number of third type of airplane number of economy class passengers ---Select--- Minimize Maximize F = (objective function) Subject to (first-class passengers) (tourist passengers) (economy-class passengers) x___ ≤, = ,≥ ,> ,or < 0, y_____ ≤, = ,≥ ,> ,or < 0, z ____≤, = ,≥ ,> ,or < (nonnegativity constraint)
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 86 first-class, 50 tourist, and 116 economy-class passengers. The first plane costs $4400 for the trip and can accommodate 44 first-class, 16 tourist, and 22 economy-class passengers; the second plane costs $5400 for the trip and can accommodate 8 first-class, 16 tourist, and 42 economy-class passengers; the third plane costs $5800 for the trip and can accommodate 20 first-class, 28 tourist, and 12 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? x = number of first class passengers number of first type of airplane y = number of tourist class passengers number of second type of airplane z = number of third type of airplane number of economy class passengers ---Select--- Minimize Maximize F = (objective function) Subject to (first-class passengers) (tourist passengers) (economy-class passengers) x___ ≤, = ,≥ ,> ,or < 0, y_____ ≤, = ,≥ ,> ,or < 0, z ____≤, = ,≥ ,> ,or < (nonnegativity constraint)
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 86 first-class, 50 tourist, and 116 economy-class passengers. The first plane costs $4400 for the trip and can accommodate 44 first-class, 16 tourist, and 22 economy-class passengers; the second plane costs $5400 for the trip and can accommodate 8 first-class, 16 tourist, and 42 economy-class passengers; the third plane costs $5800 for the trip and can accommodate 20 first-class, 28 tourist, and 12 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost?
x = number of first class passengers number of first type of airplane
y = number of tourist class passengers number of second type of airplane
z = number of third type of airplane number of economy class passengers
| ---Select--- Minimize Maximize | F =
|
(objective function) |
| Subject to |
|
(first-class passengers) |
|
|
(tourist passengers) | |
|
|
(economy-class passengers) | |
|
x___ ≤, = ,≥ ,> ,or < 0, y_____ ≤, = ,≥ ,> ,or < 0, z ____≤, = ,≥ ,> ,or < |
(nonnegativity constraint) |
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