Find an initial basic feasible solution to the following transportation problem by the North-West corner method. Verify whether your solution is optimal

Is the set of vectors {( ),3,2,1 ),1,4,3( )}2,3,2( linearly independent? Give reasons for the answer.

and C = 1[ ],2

compute A B, AC B A CB, t t + whenever defined. If you think any of these are not defined, give reasons for saying so.

A company has 5 jobs to be processed by 5 mechanics. The following table gives the return in rupees when the th i job is assigned to the th j mechanic. i,( j = ,2,1 K ).5, How should the jobs be assigned to the mechanics so as to maximize the overall return?

A businessman needs five cabinets, 12 desks and 18 shelves cleaned out. He has two part time employees, Rashid and Ruby. Ruby can clean one cabinet, three desks and three shelves in a day while Rashid can clean one cabinet, two desks and 6 shelves in one day. Rashid is paid Rs. 22 per day and Ruby is paid Rs. 25 per day. In the order to minimize the cleaning costs, for how many days should Rashid and Ruby be employed? Formulate the problem as a linear programming problem and find its solution by the graphical method.

For the following matrix game, write down the equivalent LPPs for solving the game.

For the transportation problem given below, check whether the given basic feasible solution is optimal. If not, modify the given solution and find an optimal solution and the optimal value for the problem.

Solve the following LPP by the two-phase simplex method. 

    Max 

Subject to 

Solve the 4( × )3 game with pay off matrix.

At each stage, clearly explain the steps involved.

2,1( is an optimal solution to the following LPP:

An optimal assignment of the assignment problem with cost matrix C is also an optimal assignment of the assignment problem with cost matrix . C'

The number of basic variables in a feasible solution of a transportation problem with m sources and n destinations is mn.

If the following table is obtained in the intermediate stage while solving an LPP by the Simplex method, then the LPP has an unbounded solution:

For any two square matrices A and B, AB = BA.

Obtain the first order derivative of ( ) 4L x using the appropriate recurrence relations. Take L0 (x) = 1 and 

Determine the first three coefficients in the expansion of the following function in a series of the form 

Show that

) Show that all the roots of Pn (x) = 0 are real and lie between -1 and +1

Solve the initial value problem

Determine the Laplace transform of