Linear Programming — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

Your Roll N................ 1. (a) Solve the following linear programming problem graphically: (b) Find all the basic feasible solutions of the following system of equations: (c) Show that the set S = ((x, y) € R'| 4x'+ 5y? ≤ 40) is a convex set. 2. (a) Using Simplex Method, solve the following linear programming problem: (b) Solve the following linear programming problem using Simplex Method by converting the objective function to Maximization form. (e) Solve the following linear programming problem graphically and comment on the nature of solution. 3. (a) Solve the following linear programming problem using Simplex Method : (b) Write the dual of the following linear programming problem : *,, x, ≥ 0, x, is unrestricted in sign. (c) Solve the following linear programming problem using Two-Phase method. What is the nature of solution obtained? 4. (a) Find the initial basic feasible solution for the following Transportation Problem using North-west Comer Rule and Least Cost Method. Compare the solutions obtained. (b) Show that the dual of the dual of the following linear programming problem is the primal problem. (c) Five project managers can be assigned five projects. The time taken by each manager (in hours) is given in the following table. Assign the projects to each manager so that the time taken to complete the project is minimum. Manager Projects 5. (a) Five mechanics are available to work on five different machines. Any mechanic can be assigned any machine. The cost of doing the mechanical work is given below. Assign the work for different machines so as to minimize the total cost. Jobs Machines (b) (i) What is a competitive zero-sum game? Define saddle point for a game. (i) Solve the game whose pay-off matrix is given by, (c) Obtain the initial basic feasible solution to the following transportation problem using Vogel's approximation method. Is this solution an optimal solution? If not, obtain the optimal solution. 6. (a) Using the Principle of Dominance, solve the following game (b) For the following payoff matrix, transform the zero-sum game into an equivalent linear programming problem for both the players. Is there any relation between the two problems? (c) For what value of X is the following game deterministic?