The J. Mehta Company’s production manager is planning for a series of 1-month production periods for stainless steel sinks. The demand for the next 4 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 $100 per sink. If demand in any 1 month cannot be satisfied by regular production, the production manager has three other choices: (1) he can produce up to 50 more sinks per month in overtime but at a cost of $130 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 4-month period is 450 sinks, at a cost of $150 each); or (3) he can fill the demand from his on-hand inventory. The inventory carrying cost is $10 per sink per month. Back orders are not permitted. Inventory on hand at the beginning of month 1 is 40 sinks. Set up this “production smoothing” problem as a transportation problem to minimize cost.

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MONTH DEMAND FOR STAINLESS STEEL SINKS 123 120 160 240 4 100