4. A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity of 220 passengers. The three available types of planes carry 10, 15, and 20 passengers, respectively. How many of each type of plane should be leased? Give all possible solutions. Set up the system of equations and solve using Gauss-Jordan elimination. Show all of your work and check your answer. Since there are three unkowns and you are only given enough information to set up two equations, the solution set is either inconsistent or dependent. If it is inconsistent, there is no way that 12 of these airplanes could have a combined carrying capacity of 220 passengers. Otherwise, the solution set is dependent. But that does not mean that there are infinitely many possibilities since none of the unknowns can be negative, which puts restrictions on the values of all of the variables.

4. A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity of 220 passengers. The three available types of planes carry 10, 15, and 20 passengers, respectively. How many of each type of plane should be leased? Give all possible solutions. Set up the system of equations and solve using Gauss-Jordan elimination. Show all of your work and check your answer. Since there are three unkowns and you are only given enough information to set up two equations, the solution set is either inconsistent or dependent. If it is inconsistent, there is no way that 12 of these airplanes could have a combined carrying capacity of 220 passengers. Otherwise, the solution set is dependent. But that does not mean that there are infinitely many possibilities since none of the unknowns can be negative, which puts restrictions on the values of all of the variables.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity
of 220 passengers. The three available types of planes carry 10, 15, and 20 passengers,
respectively. How many of each type of plane should be leased? Give all possible
solutions. Set up the system of equations and solve using Gauss-Jordan elimination.
Show all of your work and check your answer.
Since there are three unknowns and you are only given enough information to set up
two equations, the solution set is either inconsistent or dependent. If it is inconsistent,
there is no way that 12 of these airplanes could have a combined carrying capacity
of 220 passengers. Otherwise, the solution set is dependent. But that does not mean
that there are infinitely many possibilities since none of the unknowns can be negative,
which puts restrictions on the values of all of the variables.

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