Suppose that by using dynamic programming, we are solving the following deterministic inventory problem, which is similar to the one that we covered in class. A company knows that the demand for its product during each of the next four months will be as follows: month 1, 5 units; month 2, 3 units; month 3. 8 units: and month 4, 5 units. At the beginning of each month, the company must determine how many units (an integer) should be produced during that month. Capacity limitations allow a maximum of 8 units to be produced during each month. During a month in which any units are produced, a monthly setup cost of $20 is incurred. In addition, there is a variable cost of $1 for every unit produced. Of course, the cost of not producing any unit is zero. After the production is completed in a month, this month's demand is satisfied by using the products already in the inventory at the beginning of that month together with the products produced during that month. Assume that all demand must be met on time (no late deliveries, no unsatisfied demand). At the end of each month, a holding cost of $2 per unit in inventory is incurred. The size of the company's warehouse restricts the ending inventory for each month to 3 units at most. Assume that the inventory level at the beginning of the first month is 2 units. We are using the dynamic programming to determine a production schedule which will minimize the sum of production and holding costs incurred during the next four months. Stage t is the beginning of month t for every t = 1,2,3,4, and the state at a stage is the inventory level just before making a decision at that stage. We define the value function f(1) for the subproblem consisting of stages t,t+1.....4 and the optimal decision at stage t, x,(1), as f(1): the minimum total cost of meeting demands for months t,t +1..... 4 if the state is i at stage t where x(): the optimal number of units (integer) that should be produced during month t (to attain f,()) if the state is i at stage t.. Suppose that we have just found that f(0) = 76, f(1) = 75.f(2) = 74. f(3) = 53. What are the values of fi(2) and x, (2), respectively