Linear Programming Maths - Linear Programming

1. 59 at$\Big(\frac{9}{2},\frac{5}{2}\Big)$
   
2. 42 at (6, 0)
   
3. 49 at (7, 0)
   
4. 57.2 at (0, 5.2)
   

1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is NOT the correct explanation of A
3. A is true but R is false.
4. A is false but R is true.

1. A is true, R is true: R is a correct explanation for A.
2. A is true,R is true; R is not a correct explanation for A.
3. A is true: R is false.
4. A is false: R is true.

1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is NOT the correct explanation of A
3. A is true but R is false.
4. A is false but R is true.

1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is NOT the correct explanation of A
3. A is true but R is false.
4. A is false but R is true.

1. A is true, R is true: R is a correct explanation for A.
2. A is true,R is true; R is not a correct explanation for A.
3. A is true: R is false.
4. A is false: R is true.

1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is NOT the correct explanation of A
3. A is true but R is false.
4. A is false but R is true.

1. Objective function of a L.P.P. is:

1. A constant.
2. A function to be optimised.
3. A relation between the variables.
4. None of these.

2. Which of the following statement is correct?

1. Every LPP has at least one optimal solution.
2. Every LPP has a unique optimal solution.
3. If an LPP has two optimal solutions, then it has infinitely many solutions.
4. None of these.

3. In solving the LPP: "minimize f = 6x + 10y subject to constraints $\text{x}\geq6,\text{ y}\geq2,\text{ 2x}+\text{y}\geq10,\text{ x}\geq0,\text{ y}\geq0"$ redundant constraints are:

1. $\text{x}\geq6,\text{ y}\geq2$

2. $\text{2x}+\text{y}\geq10,\text{ x}\geq0,\text{ y}\geq0$

3. $\text{x}\geq6$

4. None of these

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

1. (0, 0)
2. (0, 8)
3. (5, 0)
4. (4, 10)

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

1. 0
2. 8
3. 12
4. -18

1. What is the point of intersection of line l₁ and l₂?

1. $\Big(\frac{40}{3},\frac{50}{3}\Big)$

2. $\Big(\frac{50}{3},\frac{40}{3}\Big)$

3. $\Big(\frac{-50}{3},\frac{40}{3}\Big)$

4. $\Big(\frac{-50}{3},\frac{-40}{3}\Big)$

2. The comer points of the feasible region shown in above graph are:

1. $(0,25),(20,0),\Big(\frac{40}{3},\frac{50}{3}\Big)$

2. $(0, 0), (25, 0), (0, 20) $

3. $(0,0),\Big(\frac{40}{3},\frac{50}{3}\Big),(0,20)$

4. $(0,0),(25,0),\Big(\frac{50}{3},\frac{40}{3}\Big),(0,20)$

3. If Z = x + y be the objective function and max Z = 30. The maximum value occurs at point:

1. $\Big(\frac{50}{3},\frac{40}{3}\Big)$
2. (0, 0)
3. (25, 0)
4. (0, 20)

4. If Z = 6x - 9y be the objective function, then maximum value of Z is:

1. -20
2. 150
3. 180
4. 20

5. If Z = 6x + 3y be the objective function, then what is the minimum value of Z?

1. 120
2. 130
3. 0
4. 150

1. Let x and y denotes the number of electronic sewing machines and manually operated sewing machines purchased by the dealer. If it is assume that the dealer purchased atleast one of the the given machines, then:

1. $\text{x}+\text{y}\geq0$
2. $\text{x}+\text{y}<0$
3. $\text{x}+\text{y}>0$
4. $\text{x}+\text{y}\leq0$

2. Let the constraints in the given problem is represented by the following inequalities.

$\text{x}+\text{y}\leq20$

$360\text{x}+240\text{y}\leq5760$

$\text{x},\text{y}\geq0$

Then which of the following point lie in its feasible region.

1. (0, 24)
2. (8, 12)
3. (20, 2)
4. None of these

3. If the objective function of the given problem is maximise z = 22x + 18y, then its optimal value occur at:

1. (0, 0)
2. (16, 0)
3. (8, 12)
4. (0, 20)

4. Suppose the following shaded region APDO, represent the feasible region corresponding to mathematical formulation of given problem.

Then which of the following represent the coordinates of one of its corner points

1. (0, 24)
2. (12, 8)
3. (8, 12)
4. (6, 14)

5. If an LPP admits optimal solution at two consecutive vertices of a feasible region, then:

1. The required optimal solution is at the midpoint of the tine joining two points.
2. The optimal solution occurs at every point on the tine joining these two points.
3. The LPP under consideration is not solvable.
4. The LPP under consideration must be reconstructed.