# Echelon Method and maximization

11) Use the echelon method to solve the system of three equations in three unknowns

x - y + 4z = 19

2c + z = 4

x + 3y + z = -5

14) Find x1 is greater than or equal to 0 and x 2 is greater than or equal to 0 such that:

2x1 + 3x2 >/60

2x1 + 5x2 </ 120

and z = 5x1 + 4x2 is maximized

(see attachment for full problem description)

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#### Solution Summary

The solution solves two problems. The first uses the echelon method to solve for three unknowns from the system of equations. The second solves for another system of equations with inequality constraints.

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