Linear Programming — DU B.Sc. (Prog) Physical Sciences courses pertaining to Mathematical Sciences Previous Year Question Papers

Graph paper will be provided. Q2(a) Use Simplex Method to solve the following Linear Programming Problem. Subject to the constraints (b) Use Simplex Method to solve the following Linear Programming Problem. (c) Using Artificial variable technique Method, solve the following Linear Programming problem. Q3 (a) Define a convex set. Examine the convexity of the set S = { (x, y) e R': xy ≤1, x ≥ 0, y ≥ 0}. (7.5) (b) Formulate the dual of the following Linear programming problem. (c) Determine the values of m and n that will make (A2, B2) a saddle point from the pay-off matrix of player A. 04(a) Minimize cost in the following assignment problem. (b) Find initial basic feasible solution by using North-West corner rule, Least Cost method and Vogel's approximation method. Compare the three solutions. (c) Solve the following cost minimizing assignment problem: Q5(a) Staring with Initial Basic feasible solution obtained using Least Cost Method, find the optimum solution to following transportation problem: Sources DI D2 D3 D4 D5 Supply (b) Find all basic feasible solutions of the following equations. (c) Solve the following Linear programming problem by using artificial variables. Q6(a) Use principle of dominance to solve the following game: (b) Convert the following game problem, involving "two-person zero-sum game" into a linear programming problem for player A and player B: (c) (i) Define the following terms in "Two person Zero-Sum" game: Maximin and minimax value for a fair game Mixed strategy (ii) Determine the saddle points) in the pay-off matrix given below.