Consider the following three-period inventory problem. At the beginning of each period, a firm must determine how many units should be produced during the current period. During a period in which x units are produced, a production cost c(x) is incurred, where c(0) = 0, and for x > 0, c(x) = 3 + 2x. Production during each period is limited to at most 4 units. After production occurs, the periods random demand is observed. Each periods demand is equally likely to be 1 or 2 units. After meeting the current periods demand out of current production and inventory, the firms end-of-period inventory is evaluated, and a holding cost of $1 per unit is assessed. Because of limited capacity, the inventory at the end of each period cannot exceed 3 units. It is required that all demand be met on time. Any inventory on hand at the end of period 3 can be sold at $2 per unit. At the beginning of period 1, the firm has 1 unit of inventory.

8) Solving this problem using dynamic programming approach, the stage and decision variables for this problem are:

a) minimize the total production, holding and back ordering costs incurred in each period, and quantity of units to be produced in each period

b) each period, and quantity of units to be produced in each period

c) each period, and minimize the total production, holding and back ordering costs incurred in each period

d) minimize the total production, holding and back ordering costs incurred in each period, and amount of inventory available in each period.

e) None of the above

9) Solving this problem using dynamic programming approach, the best production option at stage 1 is:

(a) Do not produce in period 1

b) Produce 1 unit in period 1

c) Produce 2 units in period 1

d) Produce 3 units in period 1

e) None of the above

10) Solving this problem using dynamic programming approach, the best production option at stage 2 is:

(a) Do not produce in periods 1 and 2

b) Meet the demand of period 1 in the best possible way, and produce 1 unit in period 2

c) Meet the demand of period 1 in the best possible way, and produce 2 units in period 2

d) Produce 3 units in period 1

e) None of the above

11) Solving this problem using dynamic programming approach, the best production option at stage 3 is to meet the demand for periods 1, 2, and 3 in period 3.

a) True

b) False

12) Solving this problem using dynamic programming approach, the total cost of meeting the demand of period 2 in the best possible way and producing 2 units in period 3 is:

a) $21.15

b) $22.13

c) $22.65

d) $12.65

e) None of the above

13) Solving this problem using dynamic programming approach, the cost of the optimal production strategy for this production-scheduling problem is:

a) $21.15

b) $22.13

c) $22.65

d) $12.65

e) None of the above