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The J. Mehta Company's production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows: The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $95 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices: (1) he can produce up to 35 more sinks per month in overtime but at a cost of $125 per sink: (2) he can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period is 450 sinks, at a cost of $150 each): (3) Or, he can fill the demand from his on-hand inventory (i.e. beginning inventory). The inventory carrying cost is $10 per sink per month (i.e. the cost of holding a sink in inventory at the end of the month is $10 per sink). There are 10 Sinks in Inventory at the beginning of Month 1. Setup the Production Smoothing problem with the goal of minimizing cost. Regular Production Month 1 = A Regular Production Month 2=100 Regular Production Month 3=100 Regular Production Month 4=100 Overtime Production Month 1 = Overtime Production Month 2 = Overtime Production Month 3= Overtime Production Month 4 = Purchases Month 1=0 Purchases Month 2=0 Purchases Month 3 = Purchases Month 4= Ending Inventory Month 1 = Ending Inventory Month 2 = Ending Inventory Month 3=0 Ending Inventory Month 4=0 Minimum Cost = A (Format xxxxx )