A factory buys units of a commodity three times a year. The commodity is bought at the beginning of each new period i at a purchase cost of pi per unit with i=1,2,3. The factory can store up to 5 units of the commodity and the consumption requirements are ci units per period. Based on previous figures, the following estimates have been made for the three periods: (a) Construct a network flow model with appropriate capacities and costs for this system. [6 Marks] (b) Find the best purchasing schedule, the total cost in each period and the total overall cost, assuming that the factory has 4 units of the commodity in storage at the beginning of the year. Can the consumption requirements be met? [14 Marks] A factory buys units of a commodity three times a year. The commodity is bought at the beginning of each new period i at a purchase cost of pi per unit with i=1,2,3. The factory can store up to 5 units of the commodity and the consumption requirements are ci units per period. Based on previous figures, the following estimates have been made for the three periods: (a) Construct a network flow model with appropriate capacities and costs for this system. [6 Marks] (b) Find the best purchasing schedule, the total cost in each period and the total overall cost, assuming that the factory has 4 units of the commodity in storage at the beginning of the year. Can the consumption requirements be met? [14 Marks]