M.C.Q (1 Marks)

MCQ 1511 Mark

Linear programming model which involves funds allocation of limited investment is classified as:

A
Ordination budgeting model
✓
Capital budgeting models
C
Funds investment models
D
Funds origin models.

Answer

Correct option: B.

Capital budgeting models

In linear programming, Capital budgeting models to minimize the total capital cost.
The solutions from the model are used to decide the best combination of capital resources and best times to start and finish projects and to determine the net capital cost.

View full question & answer→

MCQ 1521 Mark

The minimum value of Z = 4x + 3y subjected to the constraints $3\text{x}+2\text{y}\geq160,$ $5+2\text{y}\geq200,$$ 2\text{y}\geq80;\text{x},\text{y}\geq0$ is:

✓
220
B
300
C
230
D
None of these

Answer

Correct option: A.

220

View full question & answer→

MCQ 1531 Mark

The feasible solution of an LP problem, is ________.

✓
Must satisfies all of the problems constraints simultaneously.
B
Must be a corner point of the feasible region.
C
Need not satisfy all of the constraints, only some of them.
D
Must optimize the value of the objective function.

Answer

Correct option: A.

Must satisfies all of the problems constraints simultaneously.

The feasibe solution of a inear programming probem (LP) is a solution that must satisfy all of the problems constraints simultaniously.

View full question & answer→

MCQ 1541 Mark

The number of constraints allowed in a linear program is which of the following?

A
Less than 5
B
Less than 72
C
Less than 512
✓
Unlimited

Answer

Correct option: D.

Unlimited

There is no limit on constraints allowed in linear programming.
so the number of constraints is unlimited.

View full question & answer→

MCQ 1551 Mark

By graphical method, the solution of linear programming problem
Maximize $Z = 3x_1 + 5x_2$
Subject to
$3x_1 + 2x_2 \leq 18$
$x_1 \leq 4$
$x_2 \leq 6$
$x1 \geq 0, x2 \geq 0$, is:

A
$x_1 = 2, x_2 = 0, Z = 6$
✓
$x_1 = 2, x_2 = 6, Z = 36$
C
$x_1 = 4, x_2 = 3, Z = 27$
D
$x_1 = 4, x_2 = 6, Z = 42$

Answer

Correct option: B.

$x_1 = 2, x_2 = 6, Z = 36$

We need to maximize the function $Z = 3x_4 + 5x_2$
First, we will convert the given inequations into equations, we obtain the following equations:
$3x_1 + 2x_2 = 18, x_1 = 4, x_2 = 6, x_1 = 0$ and $x_2 = 0$
Region represented by $3x_1 + 2x_2 \leq 18:$
The line $3x_1 + 2x_2 = 18$ meets the coordinate axes at $A(6, 0)$ and $B(0, 9)$ respectively.
By joining these points we obtain the line $3X1 + 2x2 = 18.$
Clearly $(0, 0)$ satisfies the inequation $3x_1 + 2x_2 = 18.$
So the region in the plane which contain the origin represents the solution set of the inequation $3x_1 + 2x_2 \leq 18.$
Region represented by $x_1 \leq 4:$
The line $x_1 = 4$ is the line that passes through $C(4, 0)$ and is parallel to the $Y$ axis.
The region to the left of the line $x_1 = 4$ will satisfy the inequation $x_1 \leq 4.$
Region represented by $x_2 \leq 6:$
The line $x_2 = 6$ is the line that passes through $D(0, 6)$ and is parallel to the $X$ axis.
The region below the line $x_2 = 6$ will satisfy the inequation $X_2 \leq 6.$
Region represented by $x_1 \geq 0$ and $x_2 \geq 0:$
Since, every point in the first quadrant satisfies these inequations.
So, the first quadrant is the region represented by the inequations $x_1 \geq 0$ and $x_2 \geq 0.$
The feasible region determined by the system of constraints, $3x_1 + 2x_2 \leq 18, x_1 \leq 4, x_2 \leq 6, x_1 \geq 0$ and $x_2 \geq 0$ are as follows

Corner points are $O(0, 0), D(0, 6), F(2, 6), E(4, 3)$ and $C(4, 0).$
The values of the objective function at these points are given in the following table.

Points	Value of Z
$O(0, 0)$	$3(0) + 5(0) = 0$
$D(0, 6)$	$3(0) + 5(6) = 30$
$F(2, 6)$	$3(2) + 5(6) = 36$
$E(4, 3)$	$3(4) + 5(3) = 27$
$C(4, 0)$	$3(4) + 5(0) = 12$

We see that the maximum value of the objective function $Z$ is $36$ which is at $F(2, 6).$

View full question & answer→

MCQ 1561 Mark

The maximum value of Z = 3x + 4y subjected to constraints $\text{x}+\text{y}\leq4,\text{x}\geq0$ and $\text{y}\geq0$ is:

A
12
B
14
✓
16
D
None of the above

Answer

Correct option: C.

The feasible region determined by the constraints, $\text{x}+\text{y}\leq4,\text{x}\geq0,$ $\text{y}\geq0,$ is given below

O (0, 0), A (4, 0), and B (0, 4) are the corner points of the feasible region. The values of Z at these points are given below:

Corner Point	z = 3x + 4y
O(0, 0)	0
A(4, 0)	12
B(0, 4)	16

Hence, the maximum value of Z is 16 at point B (0, 4)

View full question & answer→

MCQ 1571 Mark

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

A
A constant
✓
A function to be optimised
C
A relation between the variables
D
None of these

Answer

Correct option: B.

A function to be optimised

View full question & answer→

MATHS M.C.Q (1 Marks)