Linear Programming Test

Linear Programming

This is Linear Programming Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
In a LPP, the objective function is always
  • A
    constant
  • B
    Linear
    Correct
  • C
    cubic
  • D
    quadratic
2
The optimal value of the objective function Z = ax + by may or may not exist, if the feasible region for a LPP is
  • A
    Unbounded
    Correct
  • B
    a circle
  • C
    Bounded
  • D
    a polygon
3
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
  • A
    Mean value
  • B
    Maximum value
    Correct
  • C
    Minimum value
  • D
    Upper limit value
4
In linear programming problems the function whose maxima or minima are to be found is called
  • A
    Subjective function
  • B
    Delta function
  • C
    Selection function
  • D
    Objective function
    Correct
5
In linear programming problems the optimum solution
  • A
    satisfies a set of cubic inequalities (calledconstraints)
  • B
    satisfies a set of linear inequalities (called linear constraints)
    Correct
  • C
    satisfies a set of quadratic inequalities (calledconstraints)
  • D
    satisfies a set of piecewise – linear inequalities (called constraints)
6
Maximise Z = 3x + 4y subject to the constraints: x + y ≤ 4, x ≥ 0, y ≥ 0.
  • A
    Maximum Z = 17 at (0, 5)
  • B
    Maximum Z = 16 at (0, 4)
    Correct
  • C
    Maximum Z = 19 at (1, 5)
  • D
    Maximum Z = 18 at (1, 4)
7
Minimise Z = – 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.
  • A
    Minimum Z = – 15 at (5, 1)
  • B
    Minimum Z = – 12 at (4, 0)
    Correct
  • C
    Minimum Z = – 13 at (4, 1)
  • D
    Minimum Z = – 14 at (5, 0)
8
Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
  • A
    Minimum Z = 10 at \(\left( {\frac{3}{2},\;\frac{1}{2}} \right)\)
  • B
    Minimum Z = 8 at \(\left( {\frac{3}{2},\;\frac{1}{2}} \right)\)
  • C
    Minimum Z = 7 at \(\left( {\frac{3}{2},\;\frac{1}{2}} \right)\)
    Correct
  • D
    Minimum Z = 9 at \(\left( {\frac{3}{2},\;\frac{1}{2}} \right)\) 110 V 60 Hz
9
Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.
  • A
    Maximum Z = \(\frac{{245}}{{19}}\;at\;\left( {\frac{{20}}{{19}},\;\frac{{45}}{{19}}} \right)\)
  • B
    Maximum Z = \(\frac{{255}}{{19}}\;at\;\left( {\frac{{20}}{{19}},\;\frac{{45}}{{19}}} \right)\)
  • C
    Maximum Z = \(\frac{{275}}{{19}}\;at\;\left( {\frac{{20}}{{19}},\;\frac{{45}}{{19}}} \right)\)
  • D
    Maximum Z = \(\frac{{235}}{{19}}\;at\;\left( {\frac{{20}}{{19}},\;\frac{{45}}{{19}}} \right)\)
    Correct
10
Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.
  • A
    Maximum Z = 22 at (4, 3)
  • B
    Maximum Z = 24 at (4, 3)
  • C
    Maximum Z = 20 at (4, 3)
  • D
    Maximum Z = 18 at (4, 3)
    Correct
11
Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.
  • A
    Minimum Z = 6 at all the points on the line segment joining the points (6, 0) and (0, 3).
    Correct
  • B
    Minimum Z = 8 at all the points on the line segment joining the points (6, 0) and (0, 3).
  • C
    Minimum Z = 9 at all the points (6, 0) and (0, 3).
  • D
    Minimum Z = 7 at all the points on the line segment joining the points (6, 0) and (0, 3).
12
Minimize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0
  • A
    Minimum Z = 330 at (60, 0)
  • B
    Minimum Z = 320 at (60, 0)
  • C
    Minimum Z = 300 at (60, 0)
    Correct
  • D
    Minimum Z = 310 at (60, 0)
13
Minimize Z = x + 2y subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.
  • A
    Minimum Z = 120 at all the points on the line segment joining the points (0, 50) and (20, 40)
  • B
    Minimum Z = 150 at all the points on the line segment joining the points (0, 50) and (20, 40)
  • C
    Minimum Z = 100 at all the points on the line segment joining the points (0, 50) and (20, 40)
    Correct
  • D
    Minimum Z = 140 at all the points on the line segment joining the points (0, 50) and (20, 40)
14
Maximize Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
  • A
    Maximum Z = 8 at (2, 6)
  • B
    Maximum Z = 12 at (2, 6)
  • C
    Z has no maximum value
    Correct
  • D
    Maximum Z = 14 at (2, 6)
15
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
  • A
    Minimum cost = Rs 180 at all points lying on segment joining \(\left( {\frac{8}{3},\;0} \right)\;and\;\left( {2,\frac{1}{2}} \right)\)
  • B
    Minimum cost = Rs 180 at all points lying on segment joining \(\left( {\frac{8}{3},\;0} \right)\;and\;\left( {2,\frac{1}{2}} \right)\)
  • C
    Minimum cost = Rs 170 at all points lying on segment joining \(\left( {\frac{8}{3},\;0} \right)\;and\;\left( {2,\frac{1}{2}} \right)\)
  • D
    Minimum cost = Rs 160 at all points lying on segment joining \(\left( {\frac{8}{3},\;0} \right)\;and\;\left( {2,\frac{1}{2}} \right)\)
    Correct