Question 1138582
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Minimize  C = 2x + 3y + 4z subject to {{{highlight(cross(minimize))}}} {{{highlight(cross(the))}}} {{{highlight(cross(problem))}}} <U>restrictions</U>: 
4x + 2y + z = 10
 x +  y - z = 5
x ≥ 0, y  ≥0, z ≥ 0
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<pre>
4x + 2y + z = 10       (1)
 x +  y - z =  5       (2)
x ≥ 0, y  ≥0, z ≥ 0


The idea of the solution is <U>THIS</U>: 


    The given system of two equations defines a straight line in the space (x,y,z), which is the intersection 
    of the two relevant planes in {{{R^3}}}.

    I am going to express this straight line as a parametric line of one argument and then express the OBJECTIVE function 
    as the function of the same argument


     In this way I will have a linear objective function  defined on the segment in the number line, and its minimum will be 
     at one of two endpoints of the segment.
</pre>

Having this idea and the guiding instructions clearly formulated, can you, the student, complete this assignment on your own ?