Bounded and Unbounded Feasible Region

Q. Which of the following linear programming problems with the given constraints gives an unbounded feasible region

1. None of the options given

2. A linear programming problem with the constraints x ≥ 0 y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10

3. A linear programming problem with the constraints x ≥ 0 y ≥ 0, x + 2y ≤ 8, 3x+2y ≤ 1

4. A linear programming problem with the constraints x ≥ 0 y ≥ 0, 2x+y ≥ 3, x+2y ≥ 6

Q. If $z=5x+2y$ subject to the following constraints : $x-2y\le 2,3x+2y\le 12,-3x+2y\le 3,x\ge 0,y\ge 0,$ then which of the following is/are true?

1. $z_{max}=19$
2. $z_{max}=21$
3. $z_{min}=0$
4. $z_{min}=10$

Q. Which of the following linear programming problems with the given constraints gives an unbounded feasible region

1. A linear programming problem with the constraints x ≥ 0 y ≥ 0, x + 2y ≤ 8, 3x+2y ≤ 1

2. None of the options given

3. A linear programming problem with the constraints x ≥ 0 y ≥ 0, 2x+y ≥ 3, x+2y ≥ 6

4. A linear programming problem with the constraints x ≥ 0 y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10

Q. For an LPP,
maximize $z=ax+by$ where $a,b\in R$ subject to the constraints
$a_{1}x+b_{1}y\le 0$
$a_{2}x+b_{2}y\le 0$
$x,y\ge 0$,
consider the following statements:
(I) The solution depends on the optimizing function.
(II) The solution depends on the constraints.

Which of the following statement(s) is/are correct?

1. Both (I) and (II)
2. (I) only
3. (II) only
4. The solution depends upon some more aspects.

Q. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 40), (60, 0). The objective function is
Z = 4x + 3y.
Compare the quantity in Column A and Column B
Column A Column B
Maximum of Z 325

1. The quantity in column A is greater
2. The quantity in column B is greater
3. The two quantities are equal
4. The relationship can not be determined on the basis of the information
   supplied

Q. If $Z=5x+10y,$ subject to the constraints $x+2y\le 120,$ $x+y\ge 60,$ $x-2y\ge 0$ and $x\ge 0,y\ge 0,$ then the maximum value of $Z$ occurs at

[1 mark]

1. only one point
2. only two points
3. more than two points but finite
4. infinite number of points

Q.

If ax + by=1; a, b, x, y are integers. which of the following is not true:

a) (a.b)=1

b) (x, y)=1

c) (a, y)=1

d) (b, y)=1