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KCET 2025 Math Paper

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Question : 14 of 60

Marks: +1, -0

Consider the following statements:

Statement (I): In a LPP, the objective function is always linear.

Statement (II): Ina LPP, the linear inequalities on variables are called constraints. Which of the following is correct?

Statement $(I)$ is true, Statement $(II)$ is true
Statement (I) is true, Statement (II) is false
Both Statements (I) and (II) are false
Statement $(I)$ is false, Statement $(II)$ is true

Solution:

Option A. Both statements are true.

Reasoning:

By definition, a Linear Programming Problem (LPP) has a linear objective function, for example

\max z=c_1 x_1+c_2 x_2+\cdots+c_n x_n.

The restrictions on the variables take the form of linear inequalities (or equalities), such as

a_{i1} x_1+a_{i2} x_2+\cdots+a_{in} x_n \leq b_i,

and these are called constraints.

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