Plug points into : - (0, 8): (not )
- (1, 1): (OK)
- (5, 5): (not OK)
- (2, 2): (not OK) So only (1, 1) works.
02
PYQ 2023
easy
mathematicsID: cbse-com
Minimise subject to:
Official Solution
Correct Option: (1)
Step 1: Draw lines: Step 2: Feasible region is unbounded region above both lines in first quadrant. Step 3: Find corner points of feasible region:
- Intersection of lines: solve Multiply 1st by 2: Multiply 2nd by 4: . Subtract: . Put in 2nd: . Corner point: . Also find intercepts and check minimum on boundary. Finally: Evaluate at corner points.
03
PYQ 2023
medium
mathematicsID: cbse-com
The corner points of the bounded feasible region of an LPP are O(0, 0), A(250, 0), B(200, 50) and C(0, 175). If the maximum value of the objective function occurs at the points A(250, 0) and B(200, 50), then the relation between a and b is:
1
2
3
4
Official Solution
Correct Option: (2)
The maximum of the objective function occurs at both points A and B. So, At A(250, 0): At B(200, 50): Since for maximum: Oops! Wait — but the question says , so the coefficient of is , so the calculation is correct. So, So the answer is (A) not (B). Correct option is (A).
04
PYQ 2025
hard
mathematicsID: cbse-com
Solve the following LPP graphically: Maximize: Subject to:
Official Solution
Correct Option: (1)
Step 1: Convert inequalities to equations
Line 1:
Line 2:
Line 3:
Step 2: Find Intercepts
Line 1: ,
Line 2: ,
Line 3: ,
Step 3: Graph and Feasible Region
Plot all three lines and shade the region that satisfies all constraints including and .
Step 4: Find Corner Points (Intersections)
Line 1 & Line 2: Solve: Multiply (i) by 2: Subtract from (ii): So point A:
Line 2 & Line 3: Substitute: So point B:
Line 1 & Line 3: Substitute: So point C:
Step 5: Evaluate at Each Corner Point
Point
(0, 0)
0
✅ Final Answer:
Maximum value of is at two corner points:
05
PYQ 2025
hard
mathematicsID: cbse-com
The maximum value of subject to the constraints , , is:
1
3
2
4
3
7
4
0
Official Solution
Correct Option: (2)
We are given the objective function:
Subject to the constraints:
These constraints define a feasible region in the first quadrant bounded by the line , the -axis and the -axis. Let us identify the corner points (vertices) of the feasible region: 1. When : 2. When : 3. Intersection of and : So, the corner points are: Now, evaluate at each vertex: - At :
- At :
- At : Maximum value of is:
06
PYQ 2025
medium
mathematicsID: cbse-com
In an LPP, corner points of the feasible region determined by the system of linear constraints are . If , where is to be minimized, the condition on and so that the minimum of occurs at and will be:
1
2
3
4
Official Solution
Correct Option: (2)
We are given the objective function:
and it is to be minimized over the feasible region formed by the points:
Let us evaluate at each of the corner points: At point : At point : At point : We are told that the minimum of occurs at both and . So we must have:
07
PYQ 2025
easy
mathematicsID: cbse-com
A manufacturer makes two types of toys A and B. Three machines are needed for production with the following time constraints (in minutes): Each machine is available for 6 hours = 360 minutes. Profit on A = Rupee 20, on B = Rupee 30. Formulate and solve the LPP graphically.
Official Solution
Correct Option: (1)
Step 1: Let the variables be Let = number of Toy A units produced Let = number of Toy B units produced Step 2: Write the Objective Function We want to maximize profit: Step 3: Translate constraints from machine limits
M1:
M2:
M3:
Non-negativity:
Step 4: Draw the Feasible Region Step 5: Find Corner Points of Feasible Region We solve the equations of intersecting lines to find vertices of the region: (i) Intersection of and : (ii) Intersection of and : (iii) Intersection of and : Step 6: Evaluate Objective Function at Each Corner Point Step 7: Select Optimal Value Final Answer:
