CBSE Class 12 Mathematics Linear Programming Worksheet Set B

MULTIPLE CHOICE QUESTIONS

Question. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0,40), (20,40),(60,20),(60,0).The objective function is Compare the quantity in Column A and Column B
Column A              Column B
Maximum of Z           325
(a) The quantity in column A is greater
(b) The quantity in column B is greater
(c) The two quantities are equal.
(d) The relationship cannot be determined on the basis of the information supplied.
Answer : B

Question. The feasible solution for a LPP is shown in given figure. Let Z=3x-4y be the objective function. Minimum of Z occurs at

(a) (0,0)
(b) (0,8)
(c) (5,0)
(d) (4,10)
Answer : B

Question. 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
Answer : B

Question. The set of all feasible solutions of a LPP is a ____ set.
(a) Concave
(b) Convex
(c) Feasible
(d) None of these
Answer : A

Question. 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
Answer : A

Question. 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
Answer : B

Question. In the feasible region for a LPP is ………, then the optimal value of the objective function Z = ax+bymayormaynot exist.
(a) bounded
(b) unbounded
(c) in circled form
(d) in squared form
Answer : B

Question. 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
(c) Optimal value, objective, nonnegative
(d) Objective, optimal value, nonnegative
Answer : C

Question. 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
Answer : B

Question. Region represented by x≥0,y≥0 is:
(a) First quadrant
(b) Second quadrant
(c) Third quadrant
(d) Fourth quadrant
Answer : A

Question. Z =3x + 4y, Subject to the constraints x+y 1, x,y ≥0. the shaded region shown in the figure as OAB is bounded and thecoordinatesof corner points O, A and B are (0,0),(1,0) and (0,1), respectively.

The maximum value of Z is 2.
(a) true
(b) false
(c) can’t say
(d) partially true
Answer : B

Question. 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
Answer : A

Question. The maximum value of Z = 4x+3y, if the feasible region for an LPP is as shown below, is

(a) 112
(b) 100
(c) 72
(d) 110
Answer : A

Question. The feasible region for an LPP is shown shaded in the figure. Let Z = 4x-3y be objective function. Maximum value of Z is:

(a) 0
(b) 8
(c) 30
(d) -18
Answer : C

Question. 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
Answer : B

Question. The linear programming problem minimize Z= 3x+2y,subject to constraints x+y8, 3x+5y 15, x,y ≥0, has
(a) One solution
(b) No feasible solution
(c) Two solutions
(d) Infinitely many solutions
Answer : B

Question. The graph of the inequality 2x+3y > 6 is:
(a) half plane that contains the origin
(b) half plane that neither contains the origin nor the points of the line 2x+3y =6
(c) whole XOY-plane excluding the points on the line 2x+3y =6
(d) entire XOY-plane
Answer : B

Question. 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 the feasible region
(d) None of these
Answer : C

Question. 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
Answer : B

Question. 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)
(c) (2,2/7)
(d) (0, 3)
Answer : C

Question. 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
Answer : A

Question. Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.
(a) 16 at (4, 0)
(b) 24 at (0, 4)
(c) 24 at (6, 0)
(d) 36 at (0, 6)
Answer : D

Question. Feasible region for an LPP shown shaded in the following figure. Minimum of Z = 4x+3y occurs at the point:

(a) (0,8)
(b) (2,5)
(c) (4,3)
(d) (9,0)
Answer : B

Question. 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
Answer : D

Question. Minimize Z = 13x – 15y subject to the constraints : x + y ≤ 7, 2x – 3y + 6 ≥ 0 , x ≥ 0, y ≥ 0.
(a) -23
(b) -32
(c) -30
(d) -34
Answer : C