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  • Solve the following Linear Programming Problems graphically; Z = 3x + 4y

1.    Solve the following Linear Programming Problems graphically:

          Maximise  Z = 3x + 4y 

         Subject to the constraints  x+y\leq 4,x\geq 0,y\geq 0.

         Show that the minimum of Z occurs at more than two points.

Answers (1)

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The region determined by constraints, x+y\leq 4,x\geq 0,y\geq 0. is as follows,

Chapter 12 Linear Programming Question 1

The region A0B represents the feasible region

The corner points of the feasible region are B(4,0),C(0,0),D(0,4)

Maximise  Z = 3x + 4y

 The value of these points at these corner points are : 

Corner points            Z = 3x + 4y  

        B(4,0)

               12  
       C(0,0)              0  
        D(0,4)                16 maximum

The maximum value of Z is 16  at D(0,4)

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seema garhwal

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