Exam Notes
Linear Programming Class 12 Exam Prep Revision β Grandmaster Guide
A
Ayush (Founder)
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Last Updated: 2026-04-20
- E = (xβ + xβ + ... + xβ) / n
- R = (xβ - xβ) / (xβ + xβ)
- x = (xβ + xβ) / 2
- y = (yβ + yβ) / 2
- z = (zβ + zβ) / 2
- L = xβ + xβ + ... + xβ
- W = yβ + yβ + ... + yβ
- P = zβ + zβ + ... + zβ
- C = (x - xβ) / (xβ - xβ)
- D = (y - yβ) / (yβ - yβ)
- Objective function: Z = ax + by
- Constraints: x β₯ 0, y β₯ 0, ax + by β€ c
- Corner point method: evaluate Z at each corner point
- Graphical method: plot the constraints and find the feasible region
πͺ€ The 5 Mistakes That Cost Marks
- Not checking the corner points of the feasible region
- Not considering the non-negativity constraints
- Not evaluating the objective function at each corner point
- Not plotting the constraints correctly
- Not finding the optimal solution correctly
βοΈ 3 Solved PYQs
- A company produces two products, A and B, which require two resources, labor and material
- The profit on each unit of A is 20 and on each unit of B is 30
- The labor required for each unit of A is 2 hours and for each unit of B is 3 hours
- The material required for each unit of A is 1 unit and for each unit of B is 2 units
- The total labor available is 240 hours and the total material available is 200 units
- Formulate the problem as a linear programming problem and find the optimal solution
- Let x be the number of units of A produced and y be the number of units of B produced
- The objective function is: Maximize Z = 20x + 30y
- The constraints are: 2x + 3y β€ 240, x + 2y β€ 200, x β₯ 0, y β₯ 0
- The corner points of the feasible region are: (0, 0), (120, 0), (0, 100), (60, 60)
- Evaluating the objective function at each corner point, we get: Z(0, 0) = 0, Z(120, 0) = 2400, Z(0, 100) = 3000, Z(60, 60) = 3600
- The optimal solution is x = 60, y = 60, and the maximum profit is 3600
π§ The One Thing Most Students Get Wrong
- Most students get the concept of corner point method wrong
- They think that the optimal solution will always occur at one of the corner points of the feasible region
- However, this is not always true
- The optimal solution can occur at any point on the boundary of the feasible region
- To find the optimal solution, we need to evaluate the objective function at each corner point and at each point on the boundary of the feasible region
ποΈ Ayush's Note
- To solve linear programming problems, we need to first formulate the problem
- Then, we need to find the feasible region by plotting the constraints
- Next, we need to evaluate the objective function at each corner point of the feasible region
- Finally, we need to find the optimal solution by comparing the values of the objective function at each corner point
π Last 5 Minutes Box
- Check the constraints and the objective function
- Make sure to evaluate the objective function at each corner point
- Check for any calculation errors
- Make sure to find the optimal solution correctly
- Check the units of the answer
π Practice MCQs
1. A company produces two products, A and B, which require two resources, labor and material
A) The profit on each unit of A is 10 and on each unit of B is 20
B) The labor required for each unit of A is 1 hour and for each unit of B is 2 hours
C) The material required for each unit of A is 1 unit and for each unit of B is 1 unit
D) The total labor available is 100 hours and the total material available is 100 units
Answer: B) The labor required for each unit of A is 1 hour and for each unit of B is 2 hours.
2. The objective function of a linear programming problem is
A) Maximize Z = 10x + 20y
B) Minimize Z = 10x + 20y
C) Maximize Z = 20x + 10y
D) Minimize Z = 20x + 10y
Answer: A) Maximize Z = 10x + 20y.
3. The constraints of a linear programming problem are
A) x β₯ 0, y β₯ 0, 2x + 3y β€ 240
B) x β₯ 0, y β₯ 0, x + 2y β€ 200
C) x β₯ 0, y β₯ 0, x + y β€ 100
D) x β₯ 0, y β₯ 0, 2x + y β€ 100
Answer: A) x β₯ 0, y β₯ 0, 2x + 3y β€ 240.
4. The corner points of the feasible region of a linear programming problem are
A) (0, 0), (100, 0), (0, 100)
B) (0, 0), (120, 0), (0, 100)
C) (0, 0), (60, 60), (0, 100)
D) (0, 0), (50, 50), (0, 100)
Answer: B) (0, 0), (120, 0), (0, 100).
5. The optimal solution of a linear programming problem is
A) x = 60, y = 60
B) x = 100, y = 0
C) x = 0, y = 100
D) x = 50, y = 50
Answer: A) x = 60, y = 60.
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π Academic References
Content verified against peer-reviewed research:
- οΏ½Let the People RapοΏ½: Cultural Rhetorics Pedagogy and Practices U... β Journal of Basic Writing (2019) π β DOI β
- Frustration and Hope: Examining StudentsοΏ½ Emotional Responses to ... β Journal of Basic Writing (2019) β DOI β
- Selected Performance Indicators of University-Model Schools β Aquila Digital Community (University of Southern Mississippi) (2019) π β DOI β
π = Open Access article
This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.
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