The pdf contains multiple type questions on the topic LINEAR PROGRAMMING.
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LINEAR PROGRAMMING
MULTIPLE CHOICE QUESTIONS
Q No Question
1 Corner points of the feasible region determined by the system of linear constraints are (0,3),(1,1)
and (3,0). Let Z= px+qy, where p, q>0. Condition on p and q so that the minimum of Z occurs at
(3,0) and (1,1) is
(a) p=2q (b) p=q/2
(c) p=3q (d) p=q
2 The set of all feasible solutions of a LPP is a
(a) Concave set (b) Convex set
(c) Feasible set (d) None of these
3 Corner points of the feasible region for an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5). Let F=4x+6y
be the objective function. Maximum of F – Minimum of F =
(a) 60 (b) 48
(c) 42 (d) 18
4 In a LPP, if the objective function Z = ax+by has the same maximum value on two corner points of
the feasible region, then every point on the line segment joining these two points give the
same……….value.
(a) minimum (b) maximum
(c) zero (d) none of these
5 In the feasible region for a LPP is ………, then the optimal value of the objective function Z =
ax+by may or may not exist.
(a) bounded (b) unbounded
(c) in circled form (d) in squared form
6 A linear programming problem is one that is concerned with finding the …A … of a linear function
called …B… function of several values (say x and y), subject to the conditions that the variables
are …C… and satisfy set of linear inequalities called linear constraints.
(a) Objective, optimal value, negative (b) Optimal value, objective, negative
7 Maximum value of the objective function Z = ax+by in a LPP always occurs at only one corner
point of the feasible region.
(a) true (b) false
(c) can’t say (d) partially true
ZIET, BHUBANESWAR Page 1
,8 Region represented by x 0,y 0 is:
(a) First quadrant (b) Second quadrant
(c) Third quadrant (d) Fourth quadrant
9 The feasible region for an LPP is shown shaded in the figure. Let Z = 3x-4y be objective function.
Maximum value of Z is:
(a) 0 (b) 8
(c) 12 (d) -18
10 In the given figure, the feasible region for a LPP is shown. Find the maximum and minimum value
of Z = x+2y.
(a) 8, 3.2 (b) 9, 3.14
(c) 9, 4 (d) none of these
11 Of all the points of the feasible region for maximum or minimum of objective function the points
(a) Inside the feasible region (b) At the boundary line of the
feasible region
(c) Vertex point of the boundary of (d) None of these
the feasible region
12 The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x
+ y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is
(a) 300 (b) 600
(c) 400 (d) 800
13 Z = 6x + 21 y, subject to x + 2y ≥ 3, x + 4y ≤ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z
occurs at
(a) (4, 0) (b) (28, 8)
ZIET, BHUBANESWAR Page 2
, (c) (2,2/7 ) (d) (0, 3)
14 Shape of the feasible region formed by the following constraints x + y ≤ 2, x + y ≥ 5, x ≥
0, y ≥ 0
(a) No feasible region (b) Triangular region
(c) Unbounded solution (d) Trapezium
15 The region represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 0, x ≥ 0, y ≥ 0 is
(a) unbounded (b) a polygon
(c) exterior of a triangle (d) None of these
16 Based on the given shaded region as the feasible region in the graph, at which point(s) is the
objective function Z = 3x + 9y maximum?
(A) Point B (B) Point C
(C) Point D ( D) Every point on the line segment CD
17 In the given graph, the feasible region for a LPP is shaded. The objective function
Z = 2x – 3y, will be minimum at:
ZIET, BHUBANESWAR Page 3
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