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 = beginning inventory for period j (ending inventory from period j − 1, the previous period) xj = production quantity in period j dj = demand in period j sj = ending inventory for period j choose the correct mathematical relationship or model that describes how these four variables are related. (1) sj = sj−1 − xj − dj (2) sj = sj−1 + xj − dj (3) sj−1 = sj + xj − dj (4) sj−1 = sj − xj − dj what constraint should be added if production capacity for period j is given by cj? choose the correct answer. (1) xj ≥ cj (2) xj ≤ cj (3) dj ≥ cj (4) dj ≤ cj what constraint should be added if inventory requirements for period j mandate an ending inventory of at least ij? choose the correct answer. (1) sj ≥ ij (2) sj ≤ ij (3) sj-1 ≥ ij (4) sj-1 ≤ ij check my work