Mathbee CBSE Mathbee · CBSE Class 12 Maths
CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q313 Markslinear_programming

CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 31 (Linear Programming)

Solve the following linear programming problem graphically: Minimize Z = 13x − 15y subject to constraints x + y ≤ 7, 2x − 3y + 6 ≥ 0, x ≥ 0, y ≥ 0.
Feasible polygon for x+y≤7 and 2x−3y+6≥0 in the first quadrant.
Feasible polygon for x+y≤7 and 2x−3y+6≥0 in the first quadrant.

✅ Step-by-Step Solution

Final Answer: Minimum Z = −30 at x=0, y=2.
  1. Plot constraints and find feasible region. Vertices: (0,0), (7,0), (3,4), (0,2).
  2. Evaluate Z: at (0,0)=0; (7,0)=91; (3,4)=39−60=−21; (0,2)=−30. Minimum is −30 at (0,2).
  3. Minimum Z = −30 at x=0, y=2.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Plot constraints and find feasible region. Vertices: (0,0), (7,0), (3,4), (0,2).
  • [2 marks] Evaluate Z: at (0,0)=0; (7,0)=91; (3,4)=39−60=−21; (0,2)=−30. Minimum is −30 at (0,2).
  • [0.5 marks] Minimum Z = −30 at x=0, y=2.

Master Chapter 12: Linear Programming

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Linear Programming.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Solve \((y^2-x^2)\,dx=2xy\,dy\). OR Solve…
Next Question →
Show that the line through (0,4,1) and (2,3,−1) is parallel to the…

All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/1/3

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

Related Questions in Linear Programming

Class 12 Linear Programming · Mcq Single Correct
How many feasible solutions satisfy 3x+y≤12, x+2y≤10, x,y≥0?
Class 12 Linear Programming · Mcq Single Correct
The shaded first-quadrant region lies above both x+2y=4 and x+y=3. Which constraints describe…
Class 12 Linear Programming · Mcq Single Correct
Z=ax+by has maximum 42 at (4,6) and minimum 19 at (3,2). Find a,b.
Class 12 Linear Programming · Mcq Single Correct
A bounded feasible polygon has vertices (2,72),(15,20),(40,15). For Z=18x+9y, select the…
Class 12 Linear Programming · Mcq Single Correct
How many vertices does x−y≥0, 2y≤x+2, x,y≥0 have?
Class 12 Linear Programming · Mcq Single Correct
A bounded feasible polygon has vertices (0,3),(3,2),(0,5). Find the minimum of Z=11x+7y.