Question

Consider the following statements: Statement (I): In a LPP, the objective function is always linear. Statement (II): In a LPP, the linear inequalities on variables are called constraints. Which of the following is correct?

• A. Statement (I) is true, Statement (II) is false.
• B. Both Statements (I) and (II) are false.
• C. Statement (I) is false, Statement (II) is true.
• D. Both statements (I) and (II) are true.

Hint:

When working with Linear Programming Problems (LPP), always check that the objective function and the constraints are both linear expressions involving the decision variables.

Answer 1

The Correct Option is D

- Statement (I) is true because in a Linear Programming Problem (LPP), the objective function is always linear. It is of the form \( c_1x_1 + c_2x_2 + \dots + c_nx_n \), where \( x_1, x_2, \dots, x_n \) are decision variables and \( c_1, c_2, \dots, c_n \) are constants.
- Statement (II) is also true because in an LPP, the constraints are the linear inequalities on the decision variables, such as \( a_1x_1 + a_2x_2 + \dots \leq b \), which limit the possible values of the decision variables.
Thus, both statements are true.