Models of inventory systems frequently consider the relationships among a beginning inventory, a production quantity, a demand or sales, and an ending inventory. For a given production period j, let

sj-1 = ending inventory from the previous period (beginning inventory for period j)

xj = production quantity in period j

dj = demand in period j

sj = ending inventory for period j

a. Write the mathematical relationship or model that shows ending inventory as a function of beginning inventory, production, and demand.

b. What constraint should be added if production capacity for period j is given by Cj?

c. What constraint should be added if inventory requirements for period j mandate an ending inventory of at least Ij?