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MHT CET202620 April 2026Evening ShiftMathematicsLinear ProgrammingActual

The LPP maximize z = 2x + 5y subject to x + 3y 6 , 2x + 6y 18 , x 0 , y 0 has

Options

  1. AUnique solution
  2. BInfinite solutions
  3. CNo solution
  4. DUnbounded feasible region

Correct answer

A. Unique solution

Step-by-step solution

The given constraints are: x + 3y 6 2x + 6y 18 x + 3y 9 x 0, y 0 The second constraint x + 3y 9 is redundant since x + 3y 6 is a stricter condition. The feasible region is bounded by x + 3y 6 in the first quadrant, which forms a triangle. The vertices of the feasible region are (0,0) , (6,0) , and (0,2) . Evaluating the objective function z = 2x + 5y at these vertices: At (0,0) , z = 2(0) + 5(0) = 0 At (6,0) , z = 2(6) + 5(0) = 12 At (0,2) , z = 2(0) + 5(2) = 10 The maximum value of z is 12 , which occurs exactly a

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