A manufacturing firm is planning a three month production schedule for a new product. From past production records the manager knows that 1,200 units can be produced per month. Also, an additional 400 units can be produced monthly on a overtime basis. The unit costs of items produced on a regular time basis is $15 and $20 on an overtime basis. The demands for the next 3 months are 1000, 1500, and 1800. Excess production may be stored at a cost of $1 per item per month. The manager wants to know the monthly production schedule that will minimize the total cost.
1. Formulate this problem as a regular linear programming model based on the material balance equation.
2. Formulate this problem as a transportation model.