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...

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

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 C j?

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