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MHT CET202525 Apr 2025Evening ShiftMathematicsLinear ProgrammingActual

In L.P.P. , the maximum value of objective function Z =6 x +3 y subject to constraints x+ y 5, x+2 y 4,4 x+ y 12, x, y 0 is

Options

  1. A132 7
  2. B22
  3. C15
  4. D122 7

Correct answer

B. 22

Step-by-step solution

The maximum of Z = 6x + 3y occurs at a vertex of the feasible region determined by the constraints x + y 5 , x + 2y 4 , 4x + y 12 , and x 0 , y 0 . Solving the boundary equations pairwise yields the vertices: (0,2) , (0,5) , ( 7 3 , 8 3 ) , and ( 20 7 , 4 7 ) . Evaluating Z at each vertex: At (0,2) : Z = 6 0 + 3 2 = 6 At (0,5) : Z = 6 0 + 3 5 = 15 At ( 7 3 , 8 3 ) : Z = 6 7 3 + 3 8 3 = 14 + 8 = 22 At ( 20 7 , 4 7 ) : Z = 6 20 7 + 3 4 7 = 120 7 + 12 7 = 132 7 The maximum value is 22 .

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