Question

Choose the wrong statement from the following:

• A. A LPP is an optimization problem
• B. In a LPP the constraints and objective function are linear
• C. Max z=xy+2x+3y can be a valid objective function for a LPP
• D. The optimal solution of a LPP is at one of the corner points of basic feasible solution

Answer 1

The Correct Option is C

A linear programming problem (LPP) involves optimizing a linear objective function subject to a set of linear constraints. Let's examine each statement:

• A LPP is an optimization problem.
  This statement is true because LPP focuses on optimizing (maximizing or minimizing) a linear objective function.
• In a LPP, the constraints and objective function are linear.
  True, as by definition, both the objective function and constraints are linear expressions.
• Max z=xy+2x+3y can be a valid objective function for a LPP.
  This statement is false. In LPP, the objective function must be a linear equation. Here, 'xy' introduces non-linearity, making it invalid for LPP.
• The optimal solution of a LPP is at one of the corner points of basic feasible solution.
  True. For LPPs, if an optimal solution exists, it is found at a vertex (corner point) of the feasible region.

Therefore, the wrong statement is: Max z=xy+2x+3y can be a valid objective function for a LPP.