Class 12 Math: Linear Programming Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 12 Linear Programming to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (MEDIUM)

Minimize and maximize Z = 600x + 400y Subject to the constraints: x + 2y ≤ 12; 2x + y ≤ 12; 4x + 5y ≤ 20; x≥ 0; y ≥ 0 by graphical method

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Draw the graph of 2x + y = 12 ..... (i) We get intersection of (i) with the coordinate axes at points (0,12) and (6,0) Draw the graph of x + 2y = 12 ..... (ii) We get the intersection of (ii) with the coordinate axes at points (06) and (120) Draw the graph of 4x + 5y = 20 ..... (iii) We get the intersection of (iii) with the coordinate axes at points (0,4) and (5,0) Common shaded region is the feasible region with corner points (5,0),(6,0),(4,4),(0,6),(0,4) Corner points Z = 600x + 400y (0,4) 1600 minimum (0.6) 2400 (4,4) 4000 maximum (6,0) 3600 (5,0) 3000 Hence, Minimum value of z = 1600 at (0,4) and Maximum value of z = 4000 at (4,4)

Question 2 (EASY)

Solution of LPP To maximise Z = 4x + 8y subject to constraints : 2x + y ≤ 30, x + 2y ≤ 24, x ≥ 3, y ≤ 9, y ≥ 0 is
  • Option 1: x = 12, y = 6
  • Option 2: x = 6, y = 12
  • Option 3: x = 9, y = 6
  • Option 4: none of these

Solution Explanation & Steps: (a) x = 12, y = 6

Question 3 (MEDIUM)

Solve the following problem graphically: Minimise and Maximise Z = 3x + 9y subject to the constraints: x + 3y ≤ 60; x + y ≥ 10; x ≤ y; x ≥ 0, y ≥ 0

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Plotting the inequations x + 3y ≤ 60, x + y ≥ 10, x ≤ y, x ≥ 0, y ≥ 0. We notice common shaded portion is the feasible solution. Possible points for maximumand minimum Z are A(5, 5),B(15, 15), C(0, 20), D(0, 10) Minimum Z is at A(5, 5), i.e. x = 5, y = 5, Minimum Z = 60. Maximum Z is at B(15, 15), i.e. x = 15, y = 15 and C(0, 20), i.e. x = 0, y = 20, Maximum Z = 180.

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 12 Math Resource Hub for Linear Programming: • 🧮 Interactive Solver: Solve Linear Programming Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Linear Programming Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Linear Programming PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Linear Programming Key Equations - Complete revision references. • 🔄 Next Topic Guide: Probability Study Notes • 🎓 Syllabus Overview: Class 12 Mathematics Portal - Access all chapter guides.
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