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Describe how quadratic equations can be used in decision-making.

Which of the following statements true or false? Give a short proof or a counter example in support of your answers. i) The forward and backward recursive formulation in Dynamic programming techniques can result in different optimum solutions to the same problem. ii) A non-critical activity cannot have zero total float. iii) The addition of a consultant to all the elements of an assignment problem can affect the optimal solution of the problem. iv) If the primal LPP has an unbounded solution, the dual LPP cannot have a feasible solution. v) In queuing theory, if the arrivals are according to Poisson distribution with parameter λ, the inter-arrival time is exponential with parameter e^λ.

A distribution system has the following constraints:

Factory A B C

Capacity (in units): 45 15 40

Warehouse 1 2 3

Demand (in units): 25 55 20

The transportation costs per unit (in Rs.) through each route are:

To 1 2 3

From A 10 7 8

B 15 12 9

C 7 8 12

Find an initial basic feasible solution by the North-West corner method. Starting with this solution, carry out as many iterations of the u-v method as necessary to find a basic feasible solution with transportation cost less than Rs.800.

Factory A B C

Capacity (in units): 45 15 40

Warehouse 1 2 3

Demand (in units): 25 55 20

The transportation costs per unit (in Rs.) through each route are:

To 1 2 3

From A 10 7 8

B 15 12 9

C 7 8 12

Find an initial basic feasible solution by the North-West corner method. Starting with this solution, carry out as many iterations of the u-v method as necessary to find a basic feasible solution with transportation cost less than Rs.800.

A sales manager wishes to assign four sales territories to four salespersons. The salespersons differ in their ability and skills and consequently the sales expected in each territory are different. The estimates of sales per month for each salesperson in different territories are given below:

Estimated monthly sales

Territory

1 2 3 4

Salesperson

A 20 40 45 30

B 50 40 55 40

C 45 40 42 50

D 48 50 42 45

Find the optimal assignment of the four salespersons to the four different territories and the maximum monthly sales.

Estimated monthly sales

Territory

1 2 3 4

Salesperson

A 20 40 45 30

B 50 40 55 40

C 45 40 42 50

D 48 50 42 45

Find the optimal assignment of the four salespersons to the four different territories and the maximum monthly sales.

A distribution system has the following constraints:

Factory: A B C

Capacity(in units): 45 15 40

Warehouse: 1 2 3

Demand(in units): 25 55 20

The transportation costs per unit (in Rs.)through each route are:

To

| || |||

From A 10 7 8

B 15 12 9

C 7 8 12

Find an initial basic feasible solution by the North-West Corner method. Starting with this solution, carry out as many iterations of the u-v method as necessary to find a basic feasible solution with transportation cost less than Rs.800.

Factory: A B C

Capacity(in units): 45 15 40

Warehouse: 1 2 3

Demand(in units): 25 55 20

The transportation costs per unit (in Rs.)through each route are:

To

| || |||

From A 10 7 8

B 15 12 9

C 7 8 12

Find an initial basic feasible solution by the North-West Corner method. Starting with this solution, carry out as many iterations of the u-v method as necessary to find a basic feasible solution with transportation cost less than Rs.800.

Which of the following statements are true or false? Give a short proof or a counter example in support of your answers. i) The forward and backward recursive formulation in Dynamic programming techniques can result in different optimum solutions to the same problem. ii) A non-critical activity cannot have zero total float. iii) The addition of a consultant to all the elements of an assignment problem can affect the optimal solution of the problem. iv) If the primal LPP has an unbounded solution, the dual LPP cannot have a feasible solution. v) In queuing theory, if the arrivals are according to Poisson distribution with parameter λ, the inter-arrival time is exponential with parameter e^λ.

sin inverse( xsquare /y) is a homogeneous function of x and y.True or false?

A company owns two flour mills viz. A and B, which have different production capacities for high,medium and low quality flour.The company has entered a contract to supply flour to a midium and low quality resectively .It cost the company Rs.2000 and Rs.1500 per day to run mill A and B respectively.On a day ,mill A produces 6,2 and 4 quantals of high,midium and low quality flour respectively.How many days per month should each mill be operated in order to meet the contract order most economically.

Q1. A system of linear equations is shown below.

{2x+5y+6z =4 x-6y+2z=9

3x-2y+4z=8

(a) Write down the augmented matrix for the above system of equations.

(b) Determine whether the system of equations has unique solution.

(c) Use Gaussian elimination method to solve the above system of equations.

Q2. A student wants to study the dynamic characteristics of a low-rise building under lateral loading. The student models the building by a single lumped mass model. After considering damping, stiffness and characteristics of loading, the student comes up with the following differential equation:

d^x/dt^2-6 dx/dt+8x=sin t

where x(t) is the time-dependent function for the lateral displacement of the building.

(a) Find the complementary function of the lateral displacement.

(b) Find the particular integral of the resulting displacement.

(c) Find the particular solution of the differential equation,

given that x(0)=0 and x'(0)=1.

{2x+5y+6z =4 x-6y+2z=9

3x-2y+4z=8

(a) Write down the augmented matrix for the above system of equations.

(b) Determine whether the system of equations has unique solution.

(c) Use Gaussian elimination method to solve the above system of equations.

Q2. A student wants to study the dynamic characteristics of a low-rise building under lateral loading. The student models the building by a single lumped mass model. After considering damping, stiffness and characteristics of loading, the student comes up with the following differential equation:

d^x/dt^2-6 dx/dt+8x=sin t

where x(t) is the time-dependent function for the lateral displacement of the building.

(a) Find the complementary function of the lateral displacement.

(b) Find the particular integral of the resulting displacement.

(c) Find the particular solution of the differential equation,

given that x(0)=0 and x'(0)=1.

Ques 1:

In ABC Triangle A is 90° and AC =x

If SinB=x what is sinC=?

Ques 2

-3<5-2x<7 express it with modules

In ABC Triangle A is 90° and AC =x

If SinB=x what is sinC=?

Ques 2

-3<5-2x<7 express it with modules