The Linear Programming 1 category gathers introductory problems that help you master the fundamentals of linear optimization. Topics include setting up objective functions, defining constraints, solving using the graphical method, and an introduction to the simplex algorithm. Working through these questions builds a solid base for more advanced operations‑research topics.
Look at it this way: complete solution: write formula, plug data, do arithmetic. Final value matches 0, 2. Simple and accurate.
Ref: NCERT Mathematics Class XII — Linear Programming
Understanding this is easy: we verify There will be no effect by full calculation: use standard identity, substitute, simplify step by step to reach There will be no effect.
Ref: NCERT Mathematics Class XII — Linear Programming
Notice that complete solution: write formula, plug data, do arithmetic. Final value matches The LPP has a unique optimal solution. Simple and accurate.
Ref: NCERT Mathematics Class XII — Linear Programming
The trick is using formula we get only the corner points of the feasible region. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get only the corner points of the feasible region.
Ref: NCERT Mathematics Class XII — Linear Programming
From the definition, using formula we get non-negativity constraint. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get non-negativity constraint.
Ref: NCERT Mathematics Class XII — Linear Programming
From the definition, complete solution: write formula, plug data, do arithmetic. Final value matches It will satisfy all constraints. Simple and accurate.
Ref: NCERT Mathematics Class XII — Linear Programming
Look at it this way: solving fully: apply relevant formula, put numbers, compute. Result comes as 7. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Linear Programming
We can see that we verify Infinite number of optimal solutions by full calculation: use standard identity, substitute, simplify step by step to reach Infinite number of optimal solutions.
Ref: NCERT Mathematics Class XII — Linear Programming
Applying the basic concept, using formula we get x + y ≤ 4, 3x + 8y ≤ 24, 10x + 7y ≤ 35, x ≥ 0 and y. ≥ 0subjected to Max Z = 5x + 7y. Calculation gives this
Ref: NCERT Mathematics Class XII — Linear Programming
We can see that we verify 72 by full calculation: use standard identity, substitute, simplify step by step to reach 72.
Ref: NCERT Mathematics Class XII — Linear Programming
Let's break it down: complete solution: write formula, plug data, do arithmetic. Final value matches m + 2. Simple and accurate.
Ref: NCERT Mathematics Class XII — Linear Programming
We can see that we verify Alternate optimal solution by full calculation: use standard identity, substitute, simplify step by step to reach Alternate optimal solution.
Ref: NCERT Mathematics Class XII — Linear Programming
