Ans: a
Q 2) Which of the following is correct
a) A L.P.P. always has unique solution.
b) Every L.P.P. has an optimal solution.
c) A L.P.P. admits two optimal solutions.
d) If a L.P.P. admits two optimal solutions then it has infinitely many optimal solutions.
Ans: d
Q 3) Solution set of inequality y ≥ 0 is
a) Half plane below x – axis excluding the points on the x – axis .
b) Half plane below x – axis including the points on the x – axis .
c) Half plane above x – axis .
d) None of these.
Ans: b
Q 4) Objective function of a L.P.P. is
a) Constraint
b) A function to be optimized
c) A relation between the variables.
d) None of these.
Ans: b
Q 5) Which of the following terms is not used in a linear programming problems
a) Slack variable
b) Objective function
c) Convex region
d) Feasible region
Ans: d
Q 6) The point which does not lie in half plane 2x + 3y – 12 < 0 is
a) (1, 2)
b) (2, 1)
c) (2, 3)
d) (-3, 2)
Ans: c
Q 7) Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
(a) (3, 0)
(b) (5, 6)
(c) (7, 0)
(d) (0, 5)
Ans: d
Q 8) The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5)
Let Z = px + qy, where p, q > 0. Conditions on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is
a) p = 3q
b) p = 2q
c) p = q
d) q = 3p
Ans: d
Q 9) Z = 8x + 10y, subject to 2x + y ≥ 1, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
(a) (4.5, 2)
(b) (1.5, 4)
(c) (0, 7)
(d) (7, 0)
Ans: b
Q 10) The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15), and (0, 20) is
a) p = q
b) p = 2q
c) q = 2p
d) q = 3p
Ans: d
Q 11) The solution set of the inequation 2x + y > 5 is
a) Half plane that contains the origin.
b) Open half plan not containing the origin.
c) Whole xy-plane except the point lying on the line 2x + y = 5
d) None of these
Ans: b
Q 12) The maximum value of f(x) = 4x + 3y subject to constraints x ≥ 0, y ≥ 0, 2x + 3y ≤ 18; x + y ≥ 10 is
(a) 35
(b) 36
(c) 34
(d) none of these
Ans: d
Q 13) Which of the following statement is true
a) Every L.P.P. admits an optimal solution
b) An L.P.P admits a unique solution
c) If an L.P.P admits two optimal solutions, then it has an infinite number of optimal solutions.
d) An L.P.P admits only two optimal solution
Ans: c
Q 14) Objective function of a L.P.P.is
(a) a constant
(b) a function to be optimized
(c) a relation between the variables
(d) none of these
Ans: b
Q 15) Objective function of a L.P.P is
a) a constant
b) a function to be optimized
c) a relation between the variable
d) None of these
Ans: b
Q 16) The objective function of Linear Programming Problem is
a) a polynomial
b) an equation
c) an inequation
d) None of these
Ans: a
Q 17) The optimal value of the objective function is attained at the points
(a) on X-axis
(b) on Y-axis
(c) which are comer points of the feasible region
(d) None of these
Ans: c
Q 18) The optimal value of the objective function is attained at the points
a) given by intersection of inequations with the axis only
b) given by intersection of inequations with x-axis only
c) given by corner points of the feasible region
d) None of these
Ans: c
Q 19) Region represented by x ≥ 0, y ≥ 0 is
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant
Ans: a
Q 20) The minimum value of P = 3x + y subject to 2x + 3y ≤ 6, x + y ≥ 1, x ≥ 0, y ≥ 0 is
a) 1/ 2
b) 0
c) 1
d) None of these
Ans: c
Q 21) 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
Ans: d
Q 22) The maximum value of Z = 3x + 2y, subjected to x + 2y ≤ 2, x + 2y ≥ 8; x, y ≥ 0 is
(a) 32
(b) 24
(c) 40
(d) none of these
Ans: d
Q 23) Maximize Z = 6x + 3y subject to x + y ≤ 5, x + 2y ≥ 4, 4x + y ≤ 12, x ≥ 0, y ≥ 0 is
a) 20
b) 21
c) 22
d) None of these
Ans: c
Q 24) The minimum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5 + 2y ≥ 200, 2y ≥ 80; x, y ≥ 0 is
(a) 220
(b) 300
(c) 230
(d) none of these
Ans: a
Q 25) Maximize Z = 11x + 8y, subject to x ≤ 4, y ≤ 6, x ≥ 0, y ≥ 0.
(a) 44 at (4, 2)
(b) 60 at (4, 2)
(c) 62 at (4, 0)
(d) 48 at (4, 2)
Ans: b
Q 26) The feasible, region for an LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. A minimum of Z occurs at
(a) (0, 0)
(b) (0, 8)
(c) (5, 0)
(d) (4, 10)
Ans: b
Q 27) 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)
Ans: d
Q 28) The conditions x ≥ 0, y ≥ 0 for LPP is called
a) Positive constraints
b) Non- negative constraints
c) Negative constraints
d) None of these
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