Linear Programming — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Linear Programming" — 6 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Linear Programming" — 6 important questions with detailed answers for CBSE board e…
By Syllab.in · Updated
Key Questions Covered:
- Solve the linear programming problem: Maximize z = 3x + 4y subject to x + y ≤…
- Minimize z = 2x + 3y subject to x + y ≥ 5, 2x + y ≥ 8, x ≥ 0, y ≥ 0.
- A factory produces chairs and tables. Each chair takes 2 hours and each table…
- + 3 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Solve the linear programming problem: Maximize z = 3x + 4… | ✓ Solved |
| Minimize z = 2x + 3y subject to x + y ≥ 5, 2x + y ≥ 8, x … | ✓ Solved |
| A factory produces chairs and tables. Each chair takes 2 … | ✓ Solved |
Showing 3 of 6 questions
Q1: Solve the linear programming problem: Maximize z = 3x + 4y subject to x + y ≤ 4, x ≥ 0, y ≥ 0.
To solve the LPP:
Step 1: Identify constraints.
(1) x + y ≤ 4
(2) x ≥ 0
(3) y ≥ 0
Objective: Maximize z = 3x + 4y
Step 2: Find corner points of feasible region.
Constraint (1): x + y = 4
Intersection with x = 0: (0, 4)
Intersection with y = 0: (4, 0)
Origin: (0, 0)
Corner points: (0, 0), (0, 4), ...
Q2: Minimize z = 2x + 3y subject to x + y ≥ 5, 2x + y ≥ 8, x ≥ 0, y ≥ 0.
To minimize z = 2x + 3y:
Step 1: Identify constraints and find boundary lines.
(1) x + y = 5
(2) 2x + y = 8
(3) x = 0 (y-axis)
(4) y = 0 (x-axis)
Step 2: Find intersection points.
Line 1 ∩ Line 2:
x + y = 5 ... (i)
2x + y = 8 ... (ii)
Subtracting: x = 3, y = 2
Point: (3, 2)
Line 1 ∩ y-axis (x = 0...
Q3: A factory produces chairs and tables. Each chair takes 2 hours and each table takes 3 hours. The factory has 36 hours available. Profit per chair is Rs 100 and per table is Rs 150. Maximize profit.
LPP formulation and solution:
Step 1: Define variables.
Let x = number of chairs
Let y = number of tables
Step 2: Formulate constraints.
Time constraint: 2x + 3y ≤ 36
Non-negativity: x ≥ 0, y ≥ 0
Step 3: Formulate objective function.
Maximize P = 100x + 150y
Step 4: Find corner points of feasibl...
Showing 3 of 6 questions. Visit the full page for complete solutions.