Consider the following multiperiod, multiproduct Production$-$Inventory problem. Suppose

that we are examining $$ periods $=1,...,,$ and some n products $=1,...,.$ There is an

initial inventory of $0$ that is available at hand for each product $,=1,...,.$ We need to

principally determine the level of production for each product $=1,...,$ during each of

the periods $=1,...,,$ so as to meet the forecasted demand $$ for each product $$ during

each period $$ when it occurs, at a minimal total cost. T