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MHT CET202617 April 2026Morning ShiftMathematicsLinear ProgrammingActual

For the linear programming problem, x + 2y 10, 3x + y 12, x, y 0 , the maximum value of z = 5x + 10y occurs at every point on the line segment joining the points..

Options

  1. A(0,0) and (4,0)
  2. B(0,0) and (0,5)
  3. C(4,0) and ( 14 5 , 18 5 )
  4. D(0,5) and ( 14 5 , 18 5 )

Correct answer

D. (0,5) and ( 14 5 , 18 5 )

Step-by-step solution

The given constraints are: x + 2y 10 3x + y 12 x, y 0 To find the corner points of the feasible region, we solve the equations of the boundary lines: x + 2y = 10 3x + y = 12 Multiplying the second equation by 2, we get 6x + 2y = 24 . Subtracting the first equation from this gives: 5x = 14 x = 14 5 Substituting x back into the first equation: 14 5 + 2y = 10 2y = 36 5 y = 18 5 The intersection point is ( 14 5 , 18 5 ) . The corner points of the feasible region are (0, 0) , (4, 0) , ( 14 5 , 18 5 ) , and (0, 5) . Now,

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