Caribbean Sun produces canned fruits that are sold to supermarkets. To this end, the two factories A and B of Caribbean Sun can purchase pineapples from three suppliers: Company Maximum Monthly Price Purchase Quantity Sao Paolo Farms & Co 200t 10/t Costa Rica Pineapples Inc 300t 11/t Philippines Rural 400t 9/t Assume that 1 ton (t) of fresh pineapples results in 1t of canned fruit, and that the canned fruit is sold for 40 per tonne to supermarket chains worldwide. For each ton of canned fruit, the factories also encounter direct labour costs of 25 (factory A) and 20 (factory B). Assume that factory A has a production capacity of 500t per month, while factory B has a production capacity of 350t per month. (a) Formulate a Linear Program that determines the profit-maximising production schedule. State clearly your decision variables. (10 marks) (b) Dualise the linear program from part (a), using either the direct or the indirect method. Interpret the dual problem. (10 marks) (c) Try to determine a good solution to the linear program from part (a) by inspection. Do the same for the dual problem from part (b). Looking at both solutions, what can you say about the profits of the optimal production plan for part (a)? (You don't have to find optimal solutions, but you should justify why your solutions are "good".) (13 marks)