Question:
In a graphical solution of solving Linear Programming Problem to convert inequalities into equations, they
In a graphical solution of solving Linear Programming Problem to convert inequalities into equations, they
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Watch out for the solution method specified in the question:
- If the text mentions Simplex Method $\rightarrow$ look for Slack, Surplus, or Artificial variables.
- If the text mentions Graphical Method $\rightarrow$ simply plot them by assuming them to be straight line equations!
Updated On: Jul 4, 2026
- Use slack variables
- Use surplus variables
- Use artificial surplus variables
- Assume them to be equations
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The Correct Option is D
Solution and Explanation
Concept:
When utilizing the Graphical Method to solve a two-variable Linear Programming Problem (LPP), constraints are initially defined as inequalities that bound a geometric half-space (e.g., $A_1x + B_1y \leq C_1$). To map the boundary lines of these constraints on a two-dimensional Cartesian plane, we treat the inequality as a strict equality line equation ($A_1x + B_1y = C_1$).
Step 1: Differentiating the requirements of the graphical method vs. the algebraic simplex algorithm.
Let us analyze how constraints are managed depending on the solution path chosen:
• Simplex Method Framework: This algebraic approach requires transforming inequality constraints into canonical standard forms via auxiliary variables. We add non-negative
slack variables to adjust "less-than-or-equal-to" ($\leq$) constraints, and subtract
surplus variables paired with
artificial variables to adjust "greater-than-or-equal-to" ($\geq$) constraints.
• Graphical Method Framework: This method relies on plotting boundary lines directly on a graph to isolate the feasible region. To plot an inequality line like $2x + 3y \leq 6$, we simply construct the linear plot for $2x + 3y = 6$ by identifying its coordinate intercepts.
Step 2: Concluding the proper choice.
Because the graphical approach does not require introducing auxiliary slack or surplus variables to plot the system boundaries, we simply assume the constraints to function as equations during line construction. This aligns with Option (4).
Step 1: Differentiating the requirements of the graphical method vs. the algebraic simplex algorithm.
Let us analyze how constraints are managed depending on the solution path chosen:
• Simplex Method Framework: This algebraic approach requires transforming inequality constraints into canonical standard forms via auxiliary variables. We add non-negative
slack variables to adjust "less-than-or-equal-to" ($\leq$) constraints, and subtract
surplus variables paired with
artificial variables to adjust "greater-than-or-equal-to" ($\geq$) constraints.
• Graphical Method Framework: This method relies on plotting boundary lines directly on a graph to isolate the feasible region. To plot an inequality line like $2x + 3y \leq 6$, we simply construct the linear plot for $2x + 3y = 6$ by identifying its coordinate intercepts.
Step 2: Concluding the proper choice.
Because the graphical approach does not require introducing auxiliary slack or surplus variables to plot the system boundaries, we simply assume the constraints to function as equations during line construction. This aligns with Option (4).
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