CBSE Board Examination 2024 · Section A · 1 mark

Q10: A linear programming problem optimises a linear function

Board 2024Ch 12 · Linear Programming

The question

A linear programming problem deals with the optimization of a/an :

(A) logarithmic function

(B) linear function

(D) exponential function

Exam answer

In a linear programming problem, the objective function $Z = ax + by$ is linear, and it is maximised or minimised subject to linear constraints.

Why?

"Optimization" means finding the maximum or the minimum value. In a linear programming problem the quantity being optimised is the objective function.

It is called linear because each variable appears only to the first power, multiplied by a constant, with no products such as $xy$ ⁠.

In $Z = ax + by$ ⁠, $x$ and $y$ have power $1$ ⁠. There is no $x^2$ (quadratic), no $\log x$ (logarithmic) and no $e^x$ (exponential).

Why?

For example, $Z = 3x + 2y$ is linear. $Z = x^2 + y$ would be quadratic, and that is not a linear programming problem. This rules out (A), (C) and (D).

Answer: (B) linear function

Where this comes from

Chapter 12, Linear Programming: Linear programming: the objective function.

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