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:
DEMAND FOR
MONTH STAINLESS STEEL SINKS
1 ............ 120
2 ............ 160
3 ............ 240
4 ............ 100
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); (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. Use the northwest corner rule to find an initial level for production and outside purchases over the 4-month period.