5. (a) Linear Programming is a useful Management Science technique. However, it cannot be applied everywhere. Discuss it with relevant examples. (5 marks) 5. (b) Indian Airlines is a regional airline company that flies short haul flights using small aircraft. The company has been doing very good and has decided to expand its operations. The management is in dilemma regarding whether to add some new small aircraft or start moving into pan India market with bigger aircraft. There are various factors that are likely to influence the purchase of aircraft. However, the most important decision is going to be the profitability. It is estimated that each small aircraft is going to contribute yearly profit of Rs 7 crore and each big aircraft is going to contribute yearly profit of Rs 22 crore. The cost of acquiring one small aircraft is Rs. 25 crore and the cost of acquiring one big aircraft is Rs 75 crore. The total funds available with the company is Rs. 250 crore. Further, the purchase of small aircraft is limited to a maximum of 5. (i) (ii) Formulate the LPP problem complete with explanatory statements. Solve the LPP graphically, comment on the optimal decision variables and the optimal profit that will accrue