Homework Help Forum: linear programming problem

Posted by Anonymous on Wednesday, November 26, 2008 at 8:49pm.

P=-30x+25y Subject to 2x+3y>=30 2x+y<=26 -6x+5y<=50 x,y>=0 I need the minimize and maximaze

• linear programming problem - Damon, Thursday, November 27, 2008 at 1:35pm

  One point at the origin, constrained to first quadrant. first constraint #1 2x+3y>=30 when x = 0, y = 10 when x = 15, y = 0 area above that line is in our region (are you sure your arrow is correct?) second constraint #2 2x+y<=26 when x = 0, y = 26 when x = 13, y = 0 area below that line is in third constraint #3 -6x+5y<=50 when x = 0, y = 10 when x = -50/6 or -8 1/3 , y = 0 area below that line is in sketch a graph. You see that our region of interest is a triangle from (0,10) to the intersection of #2 and #3 down to the intersection of #1 and #2 first #1 and #2 2x+3y=30 2x+y=26 gives 2 y = 4 or y = 2 then x = 12 so (12,2) now #2 and #3 2x + y=26 -->6 x + 3y = 78 -6x+5y=50 gives 8y = 128 y = 16 then x = 5 so (5,16) NOW calculate P at (5,16) and (12,2) and (0,10) and chose the biggest or smallest whichever you want. If P is "profit", you probably want the biggest.

  
  

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