Quantitative Techniques for Management — DU Bachelor of Management Studies Previous Year Question Papers

: Quantitati've. Techniques for Management Instruction.s for Candidates 2. Attempt,any five questiQjis in all. 5. Use ofstandardnormal table is allowed. 1. Consider the following Linear prQgramming problem : (i) Solve the above problem using Big M Simplex Method. (fi) Determine whether the problem has a unique optimal solut.ion or multiple optimal solutions. Justify your answer. (in) What is degeneracy? Determine whether the' solution obtained above is degenerate. ( 18) 2. (a)a What are the steps involved in the formulation of a Linear Programming model? Illustrate these steps with the help of the following situation and solve the resulting problem graphically. Mr. Gopal has received an inheritance of €95,000, which he .plans to invest for one year in two-aitematives - land and a small retail business. Each rupee invested in land yields a return of 20°/o, while each rupee invested in the retail business yields a return of 30%. Since both investments, involve risk, Mr. Gopal wants to limit his overall exposure. He estimates that the risk associated with land is 18% of the amount invested, while for the retail business it is 30°/o. He does not want the total risk rto exceed €20,000. a) A firm is considering four pricing strategies -A1, A2, A3, and A4 to compete in the market. Its competitor may respond with either an aggressive strategy 81 or a passive strategy 82. Based on market .analysis, the firm estimates that if the competitor adopts an aggressive strategy, the payoffs (in € 1akhs) corresponding to A1, A2, A3, and A4 are 2, 4,10, and 6 respectively. If the competit-or adopts a passive strategy, the corresponding payoffs are 10, 5, 2, and 4, respectively. Assuming that the situation can be modeled as a two-person zero-sum game, formulate the\ payoff matrix and solve the game using the graphical method. Determine the optimal strategies and 'the value of the game. (9+9) 3. Consider the following LPP: The final optimal solution table for the LPP is given below : (i) Write the dual to the above primal and explain the relationship .between the primal and the dual. State the solution to the dual and show that it gives the same objective function value as that of the primal. (ii) Comment' whether the constraints are binding or non-binding giving suitable justification. (iii) State the range within which change in objective function coefficients for variables X2 and X3 will not affect the optimal solution obtained above. (18) 4. A company has facto`ries at three different places S1, S2 and S3 and supply markets at four destinations D1, D2, D3 and D4. Monthly factory capacities are 250, 350 and 300 units respectively. Mdnthly requirements at demand centres are 200, 240, 210 and 250 units respectively. The per unit profit for different supply centre and market combinations are provided in the table below. For certain reasons the supply route from source S2 to market D3 is unavailable. Profit (in Rs. per unit)