Class XII

Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and
  1. each of these occurs at some points except corner points of R.
  2. each of these occurs at themidpoints of the edges of R
  3. each of these occurs at the centre of R.
  4. each of these occurs at a corner point (vertex) of R.
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).Let F = 4x + 6y be the objective function. The Minimum value of F occurs at
  1. any point on the line segment joining the points (0, 2) and (3, 0).
  2. the mid – point of the line segment joining the points (0, 2) and (3, 0) only
  3. (0, 2) only
  4. (3, 0) only
In linear programming, optimal solution
  1. satisfies all the constraints only
  2. maximizes the objective function only
  3. satisfies all the constraints as well as the objective function
  4. is not unique
Maximize Z = 3x + 4y, subject to the constraints: x + y ≤ 1, x ≥ 0, y ≥ 0.
  1. 5
  2. 3
  3. 4
  4. 6
In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is
  1. Evaluate the objective function Z = ax + by at the center point
  2. Evaluate the objective function Z = ax + by at the mid points
  3. None of these
  4. Evaluate the objective function Z = ax + by at each corner point.
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