7. [10 points] The Economic Order Quantity (EOQ) model in inventory theory assumes a constant demand rate d, an ordering cost K, a per unit purchase cost c, and an inventory holding cost h. For an order quantity Q the total cost of inventory over the horizon in the EOQ model is dk (Q) = + dc + Q hQ 2 which should be minimized to find the optimal order quantity Q*. Assume now there are n items to be ordered (i.e., j = {1,...,n}) for each of which there is a constant demand rate dj, an ordering cost K;, a per unit purchase cost cj, and an inventory holding cost hj. But space is limited to q units in the warehouse, i.e., the order quantities Q; have to vie for the limited space q. Formulate and solve the Multiple Items EOQ problem using KKT conditions (Is the problem convex?).