The 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 regular-time production cost is $ 10 / unit ($ 4 for materials, $ 1 for energy, and $ 5 for 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. Company policy is to have nothing in inventory for more than three weeks. There is a beginning inventory of 100 units and it is intended to have a ending inventory of 50 units. Units in stock have only been in stock for one week.

a) Formulate the transportation tableau that corresponds to the production planning for the next eight weeks

b) Formulate this problem as a linear programming problem under the transportation model

c) If the maximum inventory = 200 units / week, add additional restrictions to address this additional restriction.