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MHT CET20242 May 2024Morning ShiftMathematicsLinear ProgrammingActual

The point, at which the maximum value of 10 x+6 y subject to the constraints x+y 12 , 2 x+y 20, x 0, y 0 occurs, is

Options

  1. A(10,0)
  2. B(8,4)
  3. C(0,12)
  4. D(12,0)

Correct answer

B. (8,4)

Step-by-step solution

The feasible region lies on origin side of x+y=12 and 2 x+y=20 and it is in the first quadrant. The corner point of the feasible region are O (0,0), B (10,0), C (8,4), D (0,12) . At O (0,0) z =10(0)+6(0)=0 At B( 10,0 ) z=10(10)+6(0)=100 AtC (8,4) z=10(8)+6(4)=104 At D (0,12) z =10(0)+6(12)=72 Maximum value of z is 104 at it occurs at C(8,4) .

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