2- (30 pts) A 6 months contract requires production of 150, 200, 180, 140, 200, and 100 units in months 1 through 6, respectively. Production costs vary with time due to the specialized materials. Estimated production costs are $200, $400, $350, $450, $500, and $530 per unit in periods 1 through 6, respectively. To take advantage of cost variations, you may produce more units than the contract requires in some months and hold up to 500 of them in inventory for later months. But holding inventory costs $10 per unit per month. Assume there is no beginning inventory. a- Define symbolic parameters naming and indexing the constants described above. b- Formulate a time-phased linear program to compute an optimal (minimum total cost) finite- horizon, manufacturing and inventory plan for the next 6 months using the parameters of part (a). 2- (30 pts) A 6 months contract requires production of 150, 200, 180, 140, 200, and 100 units in months 1 through 6, respectively. Production costs vary with time due to the specialized materials. Estimated production costs are $200, $400, $350, $450, $500, and $530 per unit in periods 1 through 6, respectively. To take advantage of cost variations, you may produce more units than the contract requires in some months and hold up to 500 of them in inventory for later months. But holding inventory costs $10 per unit per month. Assume there is no beginning inventory. a- Define symbolic parameters naming and indexing the constants described above. b- Formulate a time-phased linear program to compute an optimal (minimum total cost) finite- horizon, manufacturing and inventory plan for the next 6 months using the parameters of part (a)