Question 1189862
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Solve the following problem by simplex method.
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Max Z = 8x1 + 16x2 
Subject to:     x1  + x2  <= 200	
                             x2  <= 125 
                       3x1 + 6x2  <= 900 	
           Where x1, x2 > 0  (non-negativity condition)
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It can be solved mentally, using common sense only 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and without using the simplex method.



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Indeed, from the objective function form  Z = 8x1 + 16x2 
it is clear that it is profitable to keep x2 as large as possible due to constrains
and after determining x2 in this way to keep x1 as large as possible due to the constrains.


Doing this way, we take  x2 = 125  (maximum allowed by the constrain x2 <= 125).


Then we determine x1 = {{{(900-6*125)/3}}} = 50 from constrain 3x1 + 6x2 <= 900.



Then  {{{Z[max]}}} = 8x1 + 16x2 = 8*50 + 16*125 = 2400.
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Solved mentally.