Consider the following multiperiod, multiproduct production-inventory problem. Suppose that we are examining T periods t=1,…,T, and some N products i=1,…,N. There is an initial inventory of yi0 that is available at hand for each product i=1,…,N. We need to principally determine the level of production for each product i=1,…,N during each of the periods t=1,…,T, so as to meet the forecasted demand dit for each product i during each period t when it occurs, at a minimal total cost. To take advantage of varying demands and costs, we are permitted to produce excess quantities to be stored for later use. However, each unit of product i consumes a storage space si, and incurs a storage cost cit during period t, for i=1,…,N, t=1,…,T. The total storage space anticipated to be available for these N products during period t is St, t=1,…,T. Furthermore, each unit of product i requires hi hours of labor to produce, where the labor cost per hour when producing a unit of product i during period t is given by lit for i=1,…,N, t=1,…,T. The total number of labor hours available to manufacture these N products during period t is given by Ht. Formulate a linear program to solve this production-inventory control system problem. Clearly specify and explain your decision variables.