Linear Programming

Comprehensive Question Bank & Study Notes

Multiple Choice Questions

1 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#971
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.
HARD
2 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#970
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)
MEDIUM
3 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#685
The corner points of the feasible region in graphical representation of a L.P.P. 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 \((2, 72)\)
MEDIUM
4 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#684
If the feasible region of a linear programming problem with objective function \(Z = ax + by\), is bounded, then which of the following is correct?
(A) It will only have a maximum value.
(B) It will only have a minimum value.
(C) It will have both maximum and minimum values.
(D) It will have neither maximum nor minimum value.
MEDIUM
5 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#683
A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function \(Z=5x+7y,\) where x and y are the number of units of X and Y respectively sold. Which of the following statement is correct?

(A) The objective function maximizes the difference of the profit earned from products X and Y.
(B) The objective function measures the total production of products X and Y.
(C) The objective function maximizes the combined profit earned from selling X and Y.
(D) The objective function ensures the company produces more of product X than product Y.
EASY
6 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#682
The corner points of the feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). If \(Z=ax+by;\) (a, \(b>0)\) be the objective function, and maximum value of Z is obtained at (0, 2) and (3, 0), then the relation between a and b is:
(A) \(a=b\)
(B) \(a=3b\)
(C) \(b=6a\)
(D) \(3a=2b\)
MEDIUM
7 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#681
For a Linear Programming Problem (LPP), the given objective function \(Z=3x+2y\) is subject to constraints: \(x+2y\le10\), \(3x+y\le15\), \(x, y\ge0\). The correct feasible region is: <div class="image-placeholder"></div>
[Image Missing]
(A) ABC
(B) AOEC
(C) CED
(D) Open unbounded region BCD
MEDIUM
8 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#680
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. \(P\equiv(\frac{3}{13},\frac{24}{13})\) \(Q\equiv(\frac{3}{2},\frac{15}{4})\) \(R\equiv(\frac{7}{2},\frac{3}{4})\) \(S\equiv(\frac{18}{7},\frac{2}{7})\). Which of the following statements is correct? <div class="image-placeholder"></div>
[Image Missing]
(A) Z is minimum at \(S(\frac{18}{7},\frac{2}{7})\)
(B) Z is maximum at \(R(\frac{7}{2},\frac{3}{4})\)
(C) (Value of Z at P) &gt; (Value of Z at Q)
(D) (Value of Z at Q) &lt; (Value of Z at R)
MEDIUM
9 Competency APPLY MCQ_SINGLE 1 Mark(s) 2025 AISSCE(Board Exam)
#679
In a Linear Programming Problem (LPP), the objective function \(Z=2x+5y\) is to be maximised under the following constraints: \(x+y\le4\), \(3x+3y\ge18\), \(x, y\ge0\). Study the graph and select the correct option. The solution of the given LPP: <div class="image-placeholder"></div>
[Image Missing]
(A) lies in the shaded unbounded region.
(B) lies in \(\Delta AOB\).
(C) does not exist.
(D) lies in the combined region of \(\Delta AOB\) and unbounded shaded region.
MEDIUM
10 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2024 AISSCE(Board Exam)
#678
A linear programming problem deals with the optimization of a/an:
(A) logarithmic function
(B) linear function
(C) quadratic function
(D) exponential function
EASY
11 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2024 AISSCE(Board Exam)
#677
The number of corner points of the feasible region determined by constraints \(x\ge0, y\ge0, x+y\ge4\) is:
(A) 0
(B) 1
(C) 2
(D) 3
MEDIUM
12 Knowledge UNDERSTAND MCQ_SINGLE 1 Mark(s) 2024 AISSCE(Board Exam)
#676
The common region determined by all the constraints of a linear programming problem is called :
(A) an unbounded region
(B) an optimal region
(C) a bounded region
(D) a feasible region
EASY
13 Knowledge REMEMBER MCQ_SINGLE 1 Mark(s) 2024 AISSCE(Board Exam)
#675
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called :
(A) feasible solutions
(B) constraints
(C) optimal solutions
(D) infeasible solutions
EASY
14 Competency APPLY MCQ_SINGLE 1 Mark(s) 2024 AISSCE(Board Exam)
#674
Of the following, which group of constraints represents the feasible region given below ?
(A) \(x+2y\le76\), \(2x+y\ge104\), \(x, y\ge0\)
(B) \(x+2y\le76\), \(2x+y\le104,\) \(x, y\ge0\)
(C) \(x+2y\ge76\), \(2x+y\le104\), \(x, y\ge0\)
(D) \(x+2y\ge76\), \(2x+y\ge104,\) \(x, y\ge0\)
MEDIUM
15 Competency APPLY MCQ_SINGLE 1 Mark(s) 2023
#855
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
MEDIUM
16 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#854
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)
MEDIUM
17 Competency APPLY MCQ_SINGLE 1 Mark(s) 2023
#835
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) $x+2y\ge4, x+y\ge3, x\le0, y\le0$
MEDIUM
18 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#834
The number of feasible solutions of the linear programming problem given as Maximize $z=15x+30y$ subject to constraints : $3x+y\le12, x+2y\le10, x\ge0, y\ge0$ is
(A) 1
(B) 2
(C) 3
(D) infinite
MEDIUM
19 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#833
16. Which of the following points satisfies both the inequations $2x+y\le10$ and $x+2y\ge8$?
(A) $(-2,4)$
(B) $(3,2)$
(C) $(-5,6)$
(D) $(4, 2)$
MEDIUM
20 Knowledge APPLY MCQ_SINGLE 1 Mark(s) 2023
#832
15. The solution set of the inequation $3x+5y<7$ is:
(A) whole $xy$-plane except the points lying on the line $3x+5y=7$.
(B) whole $xy$-plane along with the points lying on the line $3x+5y=7$.
(C) open half plane containing the origin except the points of line $3x+5y=7$.
(D) open half plane not containing the origin.
MEDIUM

Short Answer (3 Marks)

1 Competency APPLY SA 3 Mark(s) 2023
#934
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}
HARD
2 Competency APPLY SA 3 Mark(s) 2023
#928
Determine graphically the minimum value of the following objective function : $z=500x+400y$ subject to constraints $x+y\le200, x\ge20, y\ge4x, y\ge0$
HARD
3 Knowledge APPLY SA 3 Mark(s) 2023
#927
30. Solve the following linear programming problem graphically: Minimise: $z=-3x+4y$ subject to the constraints $x+2y\le8, 3x+2y\le12, x,y\ge0$
MEDIUM

Long Answer (5 Marks)

1 Competency APPLY LA 5 Mark(s) 2023
#933
Solve the following Linear Programming Problem graphically: Maximize: \(P = 70x + 40y\) subject to: \(3x + 2y ≤ 9, 3x + y ≤ 9, x ≥ 0, y ≥ 0\)
MEDIUM