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Find the max and min of the objective function f(x,y,z) = 4x + 3y + z subject to the constraints: x 0, y 0, z

Find the max and min of the objective function f(x,y,z) = 4x + 3y + z subject to the constraints:

x 0, y 0, z 0

x + y +z 1

2x + y + 2z 8

Remark: this is a linear programming problem in the 3-dimensional setting.

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