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, define s, x, and d as follows. 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 describes how these four variables are related. (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?