1. What are all necessary changes to the below model so that constraint set (1) becomes soft Give the new full model. a;, are parameters. Original OF refers to an already existing function of the decision variables that is being maximized. max Original OF m aijXij = 10 Vj = 1,...,n (1) i=1 Xij 20 Vi= 1,..,m;Vj = 1,...,n What will change if the problem becomes a minimization problem? 2. 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 y;0 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 d; 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 s, and incurs a storage cost c, 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 S, t=1,...,T. Furthermore, each unit of product i requires h; hours of labor to produce, where the labor cost per hour when producing a unit of product i during period tis given by l 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 H. Formulate a linear program to solve this production- inventory control system problem. Clearly specify and explain your decision variables.