Consider the fixed charge capacitated facility location model we discussed (or will discuss, depending on when you're reading this) in class. Recall that in this model, we are trying to select some warehouses from a set of potential warehouse sites so that fixed and variable cost is minimized, and warehouses have a capacity constraint. The model is presented below, with positive parameters f; representing the fixed cost of building at a potential site j, hirepresenting the demand at customer i, dj representing the distance from retailer i to potential site j, Krepresenting the capacity of a warehouse, and a representing the cost per unit distance per unit demand. The model also features the following variables: Yij, i=1,2,...n, j-1,2,...,m is the fraction of demand of customer i served by a warehouse at site j and xj, j=1,2,...,m is a binary variable which equals one if we locate at candidate site j, and otherwise: min 1 fjr, +=1 1 h;dij9i; s.t. {j=1 yij 1 Li=1 hiyij 0 i=1,2,...,n (1) j = 1,2,..., m (2) j = 1, 2, ..., m (3) i = 1, 2, ..., n, j = 1, 2,...,m (4) Suppose that you are trying to solve a similar problem, with a set of customers, a set of potential sites, and the same distribution costs with two changes. At each site, you can build either a small warehouse with capacity K for fixed cost f; or a large warehouse with capacity K, for fixed cost f;. Also, for each unit sold, you receive revenue of r, and your goal is to maximize profit. If it is more profitable to not serve some portion (or all) of a customer's demand, then that portion of the demand is not served. How would you modify this model to capture this situation? Note that you can change or add parameters, variables, the objective, and the constraints, as appropriate