ABC manufacturing company wishes to develop its monthly production schedule for the next three months. Depending upon the sales commitments, the company can either keep the production constant, allowing fluctuation in inventory; or its inventories can be maintained at a constant level, with fluctuating production. Fluctuating production makes overtime work necessary, the cost of which is estimated to be double the normal production cost of Rs 12 per unit. Fluctuating inventories result in an inventory carrying cost of Rs 2 per unit/month. If the company fails to fulfil its sales commitment, it incurs a shortage cost of Rs 4 per unit/month. The production capacities for the next three months are in the table:

Formulate this problem as an LP model to minimize the total production cost.