Linear Programming — DU B.A. (Prog) Mathematics as Major Previous Year Question Papers

(b) Convert the following Game Problem into a Linear Programming Problem for player A and player B and solve it by Simplex Method: Player B layer A 1 * 21 1. (a) Definera`cr6nvex +set and examine the convexity of the set n1," (b) Solve the .following LPP graphically (c) Find all the basic solutions for How should cars be assigned to customers so as to minimize the distance travelled? Also, find the minimum di st.anc.,e. (c) Six machines M], M„ M3, M4, M5 and. M6 are to be located in six places P], P2, P3, P4, P5 and P6. C;j the cost of locating machine Mf at place Pj is give.ti in.<`the natrix b.elowL:. 2. (a)7 Solve the-following linear programminYg problem by Simplex method Determine th? Qptirpum assignment schedule and find the optima_1 cost. 6. (a) Find the best strategy for each player, and the value of a play of the game A and 8. The pay-off matrix for the game is : Determine the optimum assignment schedule and find the optimal cost. (b) A car hiring company has one car at each of six depots a, b, c, d, e and f. A customer requires a car in each town namely A, B, C, D, E and F. in, Distance (in kms) between depots (origins) and towns (destinations) are given in the following distance matrix: (b) Solve the following linear programming problem by Simplex method (c) Solve the following linear programming problem by Simplex method 3. (a) Solve the following LPP graphically (b) Find the dual of the given primal problem`: (c) Write the dual for the following linear ,problem : 4. (a) Find the initial basic feasible solution using North-vyest Comer Rule, Least Cost Method and Vogel's approximation method. Compare all the three solutions. (b) Starting with initial basic feasible solution using Least Cost Method, find the optimal solution of the following transportation problem (c) Obtain the init`ial basic feasibl`e solution to the following transportation problem us'ing Vogel's approximation method. Is this solution an optimal solution? If not, obtain the optimal solution. 5. (a) Corisid-er tri6 problem of assigning fivejobs to five persons. The assignment costs are given as follows: