Solve your IGNOU Doubts

Question:

The time taken (in hours) by five different machines for completing five different jobs is given below:

Image ignouassignments-ignouacademy-com--p-solve-63668

Find the optimal assignment.

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Question:

In a factory, there are six jobs to perform each of which should go through two machines A and B in the order A B. The processing timings (in hours) for the jobs are given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T, what is the value of T?

Job	Machine A	Machine B
J₁	1	5
J₂	3	6
J₃	8	3
J₄	5	2
J₅	6	2
J₆	3	10

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Question:

Given $x_{13} = 50$ units, $x_{14} = 20$ units, $x_{21} = 55$ units, $x_{31} = 30$ units, $x_2 = 35$ units and $x_{34} = 25$ units. Is it an optimal solution to the transportation problem:

Image ignouassignments-ignouacademy-com--p-doubts-64485

If not, modify it to obtain a better feasible solution.

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Question:

Use dual simplex method to solve the following LPP:
Minimize:
$$z = 3x_1 + x_2$
Subject to the constraints:
$$x_1 + x_2 \geq 1$
$$2x_1 + 3x_2 \geq 2$
$$x_1, x_2 \geq 0.$

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Question:

Use two-phase method to solve the following LPP:
Maximize:
$$z = 3x_1 + 2x_2$
Subject to the constraints:
$$2x_1 + x_2 \leq 2$
$$3x_1 + 4x_2 \geq 12$
$$x_1, x_2 \geq 0$

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Question:

Give the dual of the following LPP:
Minimize:
$$z = 2x_1 + 3x_2 + 4x_3$
Subject to the constraints:
$$2x_1 + 3x_2 + 5x_3 \geq 2$
$$3x_1 + x_2 + 7x_3 = 3$
$$x_1 + 4x_2 + 6x_3 \leq 5$
$$x_1, x_2 \geq 0$ andx₃ is unrestricted.

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Question:

) Use simplex method to solve the following LPP:
Maximize:

$$z = 2x_1 - x_2 + x_3$

Subject to the constraints:
$$3x_1 + x_2 + x_3 \leq 60$
$$x_1 - x_2 + 2x_3 \leq 10$
$$x_1 + x_2 - x_3 \leq 20$
and $$x_1, x_2, x_3 \geq 0$ .

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Question:

Use the graphical method to solve the following LPP:
Maximize:

$$z = 2x_1 + 3x_2$
Subject to the constraints:
$$x_1 + x_2 \leq 30$
$$x_1 - x_2 \geq 0$
$$x_2 \geq 3$ $
$$0 \leq x_1 \leq 20$
and $$0 \leq x_2 \leq 12$ .

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Question:

A firm produces there product A, B and C. It uses two types of raw materials I and II of which 5000 and 7500 units respectively are available. The raw material requirements per unit of the products are given below:

Raw Material	Requirement per unit of product
Raw Material	A	B	C
I	3	4	5
II	5	3	5

The minimum demand of the three products is 600, 650 and 500 units respectively. Assuming the profits per unit of A, B and C as ₹ 50, ₹50 and ₹80 respectively. Formulate the problem as LPP model in order to determine the number of units of each product which will maximize the profit.

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Question:

Which of the following statements are true? Give reasons for your answers.
i) If an item is ordered frequently, then the risk of running out of stock is least.
ii) In deterministic queuing model, arrival rate must not exceed the service rate.
iii) The critical path of a project network represents the minimum time needed to complete the project.
iv) A necessary and sufficient condition for a basic feasible solution for a minimization LPP to be optimum is that all $Z_j - C_j \geq 0$ .
v) If dual has an unbounded solution, primal has a feasible solution.

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Question:

Alice wants to use the Digital Signature algorithm for signing messages. She chooses $p = 83$ , $q = 41$ , $g = 2$ and $a = 3$ . Alice wants to sign the message $\mathcal{M} = 20$ . She chooses the secret value $k = 8$ . Explain the procedure that Alice will use for computing the signature. What information will she send Bob?

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Question:

Alice wants to use the ElGamal digital signature scheme with public parameters $p = 47$ , $\alpha = 2$ , secret value $a = 7$ and $\beta = 34$ . She wants to sign the message $\mathcal{M} = 20$ and send it to Bob. She chooses $k = 5$ as the secret value. Explain the procedure that Alice will use for computing the signature of the message. What information will she send Bob?

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Question:

Explain how Bob will decrypt the message.
9) a) Solve the discrete logarithm problem $5^x \equiv 22 \pmod{47}$ using Baby-Step, Giant-Step algorithm.

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Question:

Alice wants to send Bob the message $\mathcal{M} = 15$ . She chooses $k = 5$ . How will she compute the cipher text? What information does she send to Bob?

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Question:

Bob uses ElGamal cryptosystem with parameters $p = 47$ , $g = 5$ and the secret value $x = 3$ . What values will he make public?

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Question:

Decrypt the message $c = 23$ that was encrypted using RSA algorithm with $e = 43$ and $n = 77$ .

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Question:

Apply runs test to the following sequence:

1001101000010000101111011
$\quad$ 0111010010110110010011010
$\quad$ 0110011100001100100111000
$\quad$ 1100001101010111101001110
$\quad$ 0010001111000001101010010
$\quad$ 1000110100000110100101101
$\quad$ 1110001001

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Question:

Apply poker test to the following sequence with level of significance $\alpha = 0.05$ .
$\quad$ 1001101000010000101111011
$\quad$ 01110100101101100100110.