Online Test — Linear Programming
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
easy
The feasible region of a LPP is the set of all points that satisfy:
Only the objective function
All the constraints including non-negativity
Only the non-negativity conditions
The objective function and one constraint
Explanation: The feasible region is the set of all points satisfying ALL constraints simultaneously, including non-negativity restrictions.
Question 2 of 10
easy
The maximum value of $Z=5x+4y$ subject to $x\le6$, $y\le4$, $x,y\ge0$ is:
30
34
46
26
Explanation: Corner points: $(0,0),(6,0),(6,4),(0,4)$. $Z(6,4)=30+16=46$. Wait, that's 46. Let me recheck: $Z(6,4)=5(6)+4(4)=30+16=46$. Option C=46 is correct.
Question 3 of 10
easy
The corner points of a feasible region are $(0,0)$, $(3,0)$, $(2,3)$, $(0,4)$. Max of $Z=2x+3y$ is:
12
9
13
6
Explanation: $Z(0,0)=0$; $Z(3,0)=6$; $Z(2,3)=4+9=13$; $Z(0,4)=12$. Max=13 at $(2,3)$.
Question 4 of 10
easy
The optimal solution to a LPP always occurs at:
A corner of the feasible region
The origin
The midpoint of the feasible region
Any interior point
Explanation: Corner Point Theorem: the optimal (max or min) value of the objective function always occurs at a corner (vertex) of the feasible region.
Question 5 of 10
medium
For an unbounded feasible region, the LPP:
Always has a maximum
Never has a minimum
May or may not have an optimal solution
Always has both max and min
Explanation: For unbounded regions: a maximum may not exist (if feasible region extends to infinity in the direction of increasing $Z$). Must check using the open half-plane test.
Question 6 of 10
medium
Minimise $Z=3x+5y$ subject to $x+y\ge2$, $x+3y\ge3$, $x,y\ge0$. Minimum is:
6
5
7
9
Explanation: Corner points (boundary intersections): $(0,2)$ on $y$-axis; $(3/2,1/2)$ intersection; $(3,0)$ on $x$-axis. $Z(0,2)=10$; $Z(3/2,1/2)=9/2+5/2=7$; $Z(3,0)=9$. Min=7. So option C=7.
Question 7 of 10
medium
A furniture maker can make chairs ($Z_1$) and tables ($Z_2$). Chairs need 2 units wood and 1 unit labour; tables need 4 units wood and 3 units labour. Available: 80 wood, 50 labour. Profit: Rs.20/chair, Rs.30/table. Which is the correct objective function?
Max $Z=20x+30y$
Max $Z=30x+20y$
Min $Z=20x+30y$
Max $Z=2x+4y$
Explanation: Let $x=$ chairs, $y=$ tables. Profit per unit: Rs.20 and Rs.30. Objective: Maximise $Z=20x+30y$.
Question 8 of 10
medium
The constraints of a LPP are $x+y\le4$, $x-y\ge0$, $x,y\ge0$. The feasible region is:
Unbounded
A triangle
A quadrilateral
A point
Explanation: Corners: $(0,0)$, $(4,0)$ (from $x+y=4, y=0$), $(2,2)$ (from $x+y=4, x=y$). Triangle with 3 corners.
Question 9 of 10
easy
Which of these is NOT a linear programming constraint?
$3x+2y\le12$
$x^2+y\le5$
$x-y\ge0$
$2x+y=10$
Explanation: $x^2+y\le5$ contains a non-linear term $x^2$. LPP constraints must be linear (no products, squares, or other non-linear terms).
Question 10 of 10
easy
The maximum value of $Z=6x+8y$ subject to $2x+3y\le6$, $x,y\ge0$ is:
16
18
24
12
Explanation: Corners: $(0,0),(3,0),(0,2)$. $Z(3,0)=18$; $Z(0,2)=16$. Max=18 at $(3,0)$. Option B=18.