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per week. Problem 2 (Steel Production Problem) (50 pts.) A steel production plant manufactures bands and coils which sell at a profit of $25 and $30 per ton, respectively. The production rate of the plant for bands is 200 tons/hr, and that for coils is 140 tons/hr. Based on the market analysis, it has been identified that the weekly demand is at most 6000 tons and 4000 tons for bands and coils, respectively. The plant operates for a maximum of 40 hours 1. Formulate a linear programming model instance for this problem, and use a computer to solve it. 2. Assume that the products need to be painted after manufacturing, and the painting department can paint at a rate of 600 tons per hour for bands and 400 tons per hour for coils. The painting department works only for 20 hours. Update the linear programming model instance to accom- modate this requirement, and re-solve the problem. 3. The plant is planning to introduce another product "rods" to its production mix with the following parameters: I Profit/ton = $40 Production volume = 150 ton/hr. Processing volume in the painting department = 350 ton/hr. Maximum amount = 4000 ton Write a new linear programming model instance. Is it profitable to include this new product for production? Comment briefly