Practice AP Inter 2nd Year Maths Study Material Chapter 12 Linear Programming MCQ to identify your strengths and weak areas.
AP Inter 2nd Year Maths Linear Programming MCQ
Question 1.
Region represented by x > 0, y ≥ 0 is
1) First quadrant
2) Second quadrant
3) Third quadrant
4) Fourth quadrant
Solution:
1) First quadrant
Region x ≥ 0, y ≥ 0 (non-negative) ⇒ Both x and y positive → first quadrant.
Question 2.
If the objective function Z = ax + by has both a maximum and a minimum value on the region R then R is
1) Bounded
2) Unbounded
3) Concave polygon
4) Infeasible
Solution:
1) Bounded
Both maximum and minimum exist only if region is closed and bounded.
Question 3.
The linear inequalities or equations or restrictions on the variables of a linear programming problem are called
1) constriants
2) Decision variables
3) objective function
4) Linear relations
Solution:
1) constriants
Linear restrictions in LPP are called constraints.
Question 4.
The optimal value of the objective function is attained at the points
1) On X-axis
2) On Y-axis
3) Which are at the corner points of the feasible region
4) Which are at the points of intersection of the inequation with Y-axis
Solution:
3) Which are at the corner points of the feasible region
In LPP, optimum value occurs at vertices of feasible region.
Question 5.
In a linear programming problem the objective function and constraints must be
1) Non-linear
2) Linear
3) Exponential
4) Logarithmic
Solution:
2) Linear
Objective function & constraints must be linear in LPP
Question 6.
The maximum value of Z = 3x + 4y subject to constraints x + y ≤ 4, x ≥ 0, y ≥ 0 is
1) 12
2) 14
3) 16
4) 10
Solution:
3) 16
Corner check points: (0, 0), (4, 0), (0, 4) then Z = 3x + 4y values: 0, 12, 16.
Maximum value is 16.
Question 7.
Maximize Z = 3x + 5y, subject to constriants x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.
1) 20 at (1, 0)
2) 30 at (0, 6)
3) 37 at (4, 5)
4) 33 at (6, 3)
Solution:
3) 37 at (4, 5)
Corner check points of feasible region. Z = 3x + 5y
Best point: (4, 5) ⇒ Z = 12 + 25 = 37
Question 8.
The point which does not lie in the half plane 2x- + 3y – 12 < 0 is
1) (2, 1)
2) (1, 2)
3) (-2, 3)
4) (2, 3)
Solution:
4) (2, 3)
Point NOT in 2x + 3y – 12 < 0
Substitute each point → LHS < 0
Check (2, 3): 4 + 9 – 12 = 1 (NOT < 0)
Question 9.
Which of the following is not a component of linear programming problem?
1) Objective function
2) Constriant
3) Decision variable
4) Differential equation
Solution:
4) Differential equation
Not a component of LPP. LPP uses linear equations, not calculus.
Question 10.
The position of points 0(0, 0) and P(2, -3) in the region of graph of inequation 2x – 3y < 5 will be
1) O inside and P outside
2) O and P both inside
3) O and P both outside
4) O outside and P inside
Solution:
1) O inside and P outside
Check points in 2x – 3y < 5
0(0, 0): 0 < 5 → inside P(2, -3): 4 + 9 = 13 > 5 → outside