Available Questions 35 found Page 1 of 2
Standalone Questions
#1478
Mathematics
Linear Programming
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
In the Linear Programming Problem for objective function $Z=18x+10y$ subject to constraints $4x+y\ge20$, $2x+3y\ge30$, $x,y\ge0$ find the minimum value of Z.
Key:
Sol:
Sol:
#1469
Mathematics
Linear Programming
VSA
2025
AISSCE(Board Exam)
2 Marks
In a Linear Programming Problem, the objective function $Z=5x+4y$ needs to be maximised under constraints $3x+y\le6$, $x\le1$, $x, y\ge0$. Express the LPP on the graph and shade the feasible region and mark the corner points.
Key:
Sol:
Sol:
#1455
Mathematics
Linear Programming
SA
REMEMBER
2025
AISSCE(Board Exam)
Competency
3 Marks
Consider the Linear Programming Problem, where the objective function $Z=(x+4y)$ needs to be minimized subject to constraints $2x+y\ge1000$, $x+2y\ge800$, $x,y\ge0$. Draw a neat graph of the feasible region and find the minimum value of Z.
Key:
Sol:
Sol:
#1432
Mathematics
Linear Programming
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
In the Linear Programming Problem (LPP), find the point/points giving maximum value for $Z=5x+10y$ subject to constraints $x+2y\le120$, $x+y\ge60$, $x-2y\ge0$, $x, y\ge0$.
Key:
Sol:
Sol:
#1414
Mathematics
Linear Programming
SA
REMEMBER
2025
AISSCE(Board Exam)
Competency
3 Marks
Solve the following Linear Programming Problem using graphical method: Maximise $Z=100x+50y$ subject to the constraints $3x+y\le600$, $x+y\le300$, $y\le x+200$, $x\ge0$, $y\ge0$.
Key:
Sol:
Sol:
#1387
Mathematics
Linear Programming
SA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
3 Marks
Solve the following linear programming problem graphically: Minimise $Z=x-5y$ subject to the constraints: $x-y\ge0$, $-x+2y\ge2$, $x\ge3$, $y\le4$, $y\ge0$.
Key:
Sol:
Sol:
#1363
Mathematics
Linear Programming
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following linear programming problem graphically: Maximise $Z=x+2y$ Subject to the constraints: $x-y\ge0$, $x-2y\ge-2$, $x\ge0$, $y\ge0$.
Key:
Sol:
Sol:
#1354
Mathematics
Linear Programming
LA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
5 Marks
Solve the following L.P.P. graphically: Maximise $Z=60x+40y$ Subject to $x+2y\le12$, $2x+y\le12$, $4x+5y\ge20$, $x,y\ge0$
Key:
Sol:
Sol:
#1323
Mathematics
Linear Programming
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following linear programming problem graphically: Maximise $Z=2x+3y$ subject to the constraints: $x+y\le6$, $x\ge2$, $y\le3$, $x,y\ge0$
Key:
Sol:
Sol:
#1302
Mathematics
Linear Programming
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Solve the following linear programming problem graphically: Maximise $z=500x+300y,$ subject to constraints $x+2y\le12$, $2x+y\le12$, $4x+5y\ge20$, $x\ge0$, $y\ge0$
Key:
Sol:
Sol:
#1258
Mathematics
Linear Programming
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following linear programming problem graphically: Maximise $z=4x+3y.$ subject to the constraints $x+y\le800$, $2x+y\le1000$, $x\le400$, $x,y\ge0$.
Key:
Sol:
Sol:
#971
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximised under the following constraints :$x + y \leq 4$, $3x + 3y \geq 18$, $x, y \geq 0$
Study the graph and select the correct option.
(A) lies in the shaded unbounded region.
(B) lies in $\triangle AOB$.
(C) does not exist.
(D) lies in the combined region of $\triangle AOB$ and unbounded shaded region.
Key: C
Sol:
Sol:
The feasible region of a Linear Programming Problem is the set of points that satisfy all the given constraints simultaneously.Constraint 1 requires the points to be in the region where the sum of $x$ and $y$ is less than or equal to 4.Constraint 2 requires the points to be in the region where the sum of $x$ and $y$ is greater than or equal to 6.Mathematically, a number cannot be both $\le 4$ and $\ge 6$ at the same time. Visually, looking at the graph, there is a clear gap between the shaded region $\Delta AOB$ and the shaded unbounded region above $PQ$. The two regions do not overlap.3. ConclusionSince there is no common region that satisfies all constraints, the feasible region is an empty set.Without a feasible region, there are no valid values for $x$ and $y$ to substitute into the objective function $Z$. Therefore, an optimal solution (maximum value) cannot be found.Answer:The correct option is (C) does not exist.
#970
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
For a Linear Programming Problem (LPP), the given objective function is $Z = x + 2y$. The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph.Which of the following statements is correct ?
(A) Z is minimum at $(\frac{18}{7}, \frac{2}{7})$
(B) Z is maximum at R$(\frac{7}{2}, \frac{3}{4})$
(C) (Value of Z at P) > (Value of Z at Q)
(D) (Value of Z at Q) < (Value of Z at R)
Key:
Sol:
Sol:
#934
Mathematics
Linear Programming
SA
APPLY
2023
Competency
3 Marks
Solve graphically the following linear programming problem : Maximise \(z = 6x + 3y\), subject to the constraints\begin{align}
4x + y &\ge 80 \\
3x + 2y &\le 150 \\
x + 5y &\ge 115 \\
x, y &\ge 0
\end{align}
4x + y &\ge 80 \\
3x + 2y &\le 150 \\
x + 5y &\ge 115 \\
x, y &\ge 0
\end{align}
Key:
Sol:
Sol:
#933
Mathematics
Linear Programming
LA
APPLY
2023
Competency
5 Marks
Solve the following Linear Programming Problem graphically: Maximize: \(P = 70x + 40y\) subject to: \(3x + 2y ≤ 9, 3x + y ≤ 9, x ≥ 0, y ≥ 0\)
Key:
Sol:
Sol:
#928
Mathematics
Linear Programming
SA
APPLY
2023
Competency
3 Marks
Determine graphically the minimum value of the following objective function : $z=500x+400y$ subject to constraints $x+y\le200, x\ge20, y\ge4x, y\ge0$
Key:
Sol:
Sol:
#927
Mathematics
Linear Programming
SA
APPLY
2023
KNOWLEDGE
3 Marks
30. Solve the following linear programming problem graphically: Minimise: $z=-3x+4y$ subject to the constraints $x+2y\le8, 3x+2y\le12, x,y\ge0$
Key:
Sol:
Sol:
#855
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
Competency
1 Marks
The number of corner points of the feasible region determined by the constraints x-y\ge0, 2y\le x+2, x\ge0, y\ge0 is:
(A) 2
(B) 3
(C) 4
(D) 5
Key:
Sol:
Sol:
#854
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
The corner points of the feasible region in the graphical representation of a linear programming problem are (2, 72), (15, 20) and (40, 15). If z=18x+9y be the objective function, then :
(A) z is maximum at (2, 72), minimum at (15, 20)
(B) z is maximum at (15, 20), minimum at (40, 15)
(C) z is maximum at (40, 15), minimum at (15, 20)
(D) z is maximum at (40, 15), minimum at (2, 72)
Key:
Sol:
Sol:
#835
Mathematics
Linear Programming
MCQ_SINGLE
APPLY
2023
Competency
1 Marks
The feasible region of a linear programming problem is shown in the figure below: ... Which of the following are the possible constraints?
(A) $x+2y\ge4, x+y\le3, x\ge0, y\ge0$
(B) $x+2y\le4, x+y\le3, x\ge0, y\ge0$
(C) $x+2y\ge4, x+y\ge3, x\ge0, y\ge0$
(D) $x+2y\ge4, x+y\ge3, x\le0, y\le0$
Key:
Sol:
Sol: