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a) Explain steps involved in operation research (5marks) b)Discuss characteristics of operation research and limitation (5marks) c) A retailer deals in two items only, item A and item B. He has 50000 to invest and a space to store at most 60pieces.An item A costs him 2500 and B costs 500,A net profit to him on item A is 500 ,and item B is 150 .If he can sell all the items he purchases, how should he invest his amount to have maximum profit? i) Give mathematical formulation to the LLP (5marks) ii)Use graphical method to solve problem (5marks) d) i)Explain general procedure for sensitivity analysis (5marks) ii)The essence of duality theory (5marks) iii)Primal dual relationship (5marks) e) Draw the network of the project whose activities and their precedence relationship are as given below; (10marks) Activities; A B C D E F G H I Predecessors - A A D BCE F E G,H F) Write a note on crashing of a project network (5marks) Please include references to your work