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Question 3 (11 marks) A manufacturer of face masks mass produces them at 4 of its plants for its 5 different retail customers. Unfortunately, it is not able to produce enough face masks to meet the demands of all its customers and it is now considering no longer producing these face masks for all 5 of these customers. Currently, the following table contains most of the information necessary to make manufacturing decisions for the upcoming planning period (3 months). Profits/1000 masks ($): Plant E capacities (1000's) 40 810 1 2 retail customer B C D 600 725 585 725 785 620 740 655 600 720 620 70 100 90 730 70 675 725 850 700 80 3 95 640 730 795 60 4 45 Demands (1000's) . Additional information: it costs $3000 per planning period for keeping customers B, D and E as customers and $2000 per period for keeping customers A and C a customer must be guaranteed at least 3000 masks if it is not dropped from the manufacturer Using Xs (in 1000's) as the amounts shipped from plant (row i) to customer j (column j), and A, B, C, D and E as the variables to determine whether or not to keep customers A, B, formulate the following in order to maximize total profits. a) The objective function (you can use '...' after the first 2 Xi's and before the last 2 xi's) if customers may be dropped by the manufacturer b) The basic (i.e., shipping) constraint for plant 1 c) The basic (i.e., demand) constraint for customer B assuming all customers will continue receiving shipments d) The demand constraint for customer A assuming that customers may be dropped e) The constraint that at least 2 (1000's) must be shipped from plant 4 to retail customer B f) The amount shipped from plant 4 to customer A must be within 2 (1000's) of the amount shipped from plant 2 to customer C g) No more than twice as many units must be shipped from plant 3 to customer B as is shipped from plant 4 to customer B