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A beverage can manufacturer makes three sizes of soft drink cans Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 105 production hours per day, and the daily supply of metal, no more than 200 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans for each size. Cans Large Medium Small Maximum Metal (kg)/batch 9 6 5 200 Machines' Time (hr)/batch 4.4 4.2 4 105 Profit/batch $51 $40 $42 a. Develop a linear programming model by identifying the variables, writing the objective function b. Write all necessary constraints c. Find the maximized profit and determine how many batches of each can size should be produced