A Linear Programming Problem (LPP) consists of which of the following components?

(A) Decision variables

(B) The graphical compliment

(C) The objective function

(D) The linear constraints

Choose the correct answer from the options given below:

A Linear Programming Problem (LPP) requires specific components to be properly defined.

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Decision variables are the unknowns to be determined in the problem, typically represented as $x$, $y$, $z$, etc. These variables represent the quantities being optimized.

For example, if determining production quantities, $x$ might represent units of Product A and $y$ might represent units of Product B.

Decision variables are essential to any LPP as they define what is being solved.

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The graphical complement refers to a graphical solution method used to solve LPPs by plotting constraints and finding optimal points visually.

This is a solution technique, not a component of the problem itself. An LPP exists independently of the method used to solve it, whether graphical, simplex, or any other method.

The graphical complement is not an essential component of an LPP.

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The objective function represents the goal to be achieved, expressed as a linear function to be maximized or minimized.

For example: Maximize $Z = 50x + 40y$ or Minimize $C = 20x + 30y$

Without an objective function, there is no purpose or direction for solving the problem.

The objective function is essential to any LPP.

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Linear constraints are the restrictions or limitations on the decision variables, expressed as linear equations or inequalities.

For example: $x + 2y \leq 100$, $x \geq 0$, $y \geq 0$

Constraints define the feasible region and ensure realistic, practical solutions. Without constraints, optimal values could be unbounded.

Linear constraints are essential to any LPP.

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The essential components of a Linear Programming Problem are:

• Decision variables (A)
• Objective function (C)
• Linear constraints (D)

The graphical complement (B) is a solution method, not a component.

Therefore, the correct answer is (A), (C) and (D) only.