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

S_j1

=

beginning inventory for period j (ending inventory from period j 1, the previous period)

x_j

=

production quantity in period j

d_j

=

demand in period j

S_j

=

S_j =ending inventory for period j

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

(1)	Sj = Sj1 xj dj
(2)	Sj = Sj1 + xj dj
(3)	Sj1 = Sj + xj dj
(4)	Sj1 = 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 I_j? Choose the correct answer.

(1)	Sj Ij
(2)	Sj Ij
(3)	Sj-1 Ij
(4)	Sj-1 Ij