Question

For the problem max Z = ax + by, x≥0, y ≥0, which of the following is NOT a valid constraint to make it a linear programming problem?

• A. x≤5,y≤10
• B. 2x+3y≤60
• C. x+2y≤40
• D. x²+y≤50

Answer 1

The Correct Option is D

In a linear programming problem, all constraints must be expressed in linear form. Linear equations or inequalities have variables that are to the power of one, meaning no variable is squared, cubic, or raised to any non-linear power.

Let us evaluate each given option to determine its linearity:

• Option 1:
  x≤5, y≤10
  This constraint is linear because both x and y are to the power of one.
• Option 2:
  2x+3y≤60
  This constraint is linear. The coefficients of the variables and the constant do not affect linearity.
• Option 3:
  x+2y≤40
  This is also a linear constraint for the same reason as above.
• Option 4:
  x²+y≤50
  This constraint is non-linear because x is squared. In a valid linear programming constraint, all variable terms should be of degree one.

Thus,

x²+y≤50

is not a valid constraint for a linear programming problem.