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  • Solve the following linear programming problem graphically : Maximise under the following constraints

Solve the following linear programming problem graphically :
Maximise Z= 34x+45y
under the following constraints
x+y\leq 300
2x+3y\leq 70
x\geq 0,y\geq 0

 

 

 

 
 
 
 
 

Answers (1)

we have, Maximize Z= 34x+45y
subject to the constraints:
x+y\leq 300 , 2x+3y\leq 70, x\geq 0, y\geq 0
converting the given inequalities into equations we obtain the following equations
x+y= 300 , 2x+3y= 70, \; Then\; x+y= 300 is  2x+3y= 70  

x 0 300
y 300 0

 

x 0 35
y \frac{70}{3} 0

                                                

ploting there points on the graph, we get the shaded fearible region ie OCDO
      corner point                                          value of  Z= 34x+45y
     O (0,0)                                                   34(0) + 45(0) = 0
    C (35,0)                                                 34(35)+45(0) = 1190
     D(0,70/3)                                                  34(0)+45(70/3) = 1050
Clearly the maximum value of Z is 1190 at (35,0)

Posted by

Ravindra Pindel

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