2. "Formulettes" Consider the following continuous, nonnegative decision variables: xg,f,p= barrels of gasoline g from tankf sold in period p Ig,f,p= barrels of gasoline g from tank f in inventory at the end of period p where g=1,2,3,4;f=1,,10; and p=1,2,3,4,5. Express each of the following using a system of linear programming constraints. How many constraints are in each system? a) Each period, sell no more than 10,000 barrels of regular gasoline (g=4). b) In period 5, the total inventory of regular gasoline (g=4) in tanks 4, 5, and 6 must be a least 20,000 barrels. c) Each period, sell at most 2 barrels of premium gasoline (g=2) for every barrel of regular (gasoline g=4) d) The barrels of each gasoline sold each period from each tank cannot exceed the inventory from the prior period. e) Write the inventory balance constraints for each period (i.e., keep track of the inventory of each type of gasoline in each tank). Assume that no new gasoline is added to the tanks. f) Each period, regular gasoline (g=4) must not be more than 70% of all gasoline sold