5.(a) For the next festive season two competing firms (firm A and Firm B) are drawing their promotional plans. Both believe that their decision making is happening under a two-person constant sum game environment with both sides having perfect information. The corresponding zem-sum game has the following pay-o ff matrix Firm B plans Aggressive 300 320 335 Normal Moderate 310 390 330 Aggressive Firm A 395 Find the optimal strategies for both the firms An investment company is planning to invest Rs. 1 Crore in various securities for a period of one year. Tt has collected the necessary information in this regand which is as follows: (b) DividendMarket Risk for one rupee Securities Face Present Value Market (Rs. Value (Rs.) value after onInvestment year (Rs.) Equity #1 | 10 Equity #2 | 100 Deben- 25 40 160 1005 150 1000980 15% (Com half yearly) Govt 5000 4y 50U0 (tax free) The management has decided the following policies about the investment programme: (a) Investment in equities should not exceed more than 60% of total investment (b) Investment in Govt. bonds must be at least Rs. 10 lakhs (c) Total risk points should not exceed 20,000. (d) Once an investment is made it will not be realized before one year Formulate this problem as a goal-programming problem. Page 4 of 5