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. To take advantage of varying demand and costs, we are permitted to produce excess quantities to be stored for later use. However, each unit of product $$ consumes storage space $,$ and incurs storage cost of $$ during $,$ for $=1,...,,=1,...,.$ The total storage space anticipated to be available for these $$ products during period $$ is $,=1,...,.$ Furthermore, each unit of product $$ requires $$ hours of labor to produce, where the labor cost per hour when producing a unit of product $$ during period $$ is given by $,$ for $=1,...,,=1,...,.$ The total number of labor hours available to manufacture these $$ products during period $$ is given by $.$ Formulate a linear program to solve this production$-$inventory control system problem, prescribing production as well as inventory levels for each product over each time period.