CBA company is planning production for the next 8 weeks. The demand is as follows: 700, 800, 900, 500, 1100, 1000, 800 and 900 respectively. The production capacity in regular time is 800 units per week. In overtime, 200 extra units can be produced. The cost of production in regular time is $ 10 unit ($ 4 materials, $ 1 energy, $ 5 labor). Labor is paid 1.5 times overtime. The cost of keeping a unit in inventory is $ 1.00 per week. The maximum delay allowed is two weeks. It is company policy to have nothing in inventory for more than three weeks. There is an initial inventory of 100 units and an ending inventory of 50 units is intended. Units in stock have only been in stock for one week. $2 un/ wkly.

1. Formulate the transportation table that corresponds to the production planning for the next 8 weeks.

2. Formulate this problem as a linear programming problem under the transportation model.

3. If the inventory has a maximum of 200 units per week. Add additional restrictions to address that additional restriction.