(Solution) - Models of inventory systems frequently consider the relationship -(2025 Original AI-Free Solution)

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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?