2. (13 points) Consider a generalized EOQ model (continuous review, deterministic demand inventory model) in which shortages are allowed, but only a fraction "q" of the shortages can ackordered and the remaining fraction "1-q" is lost forever. Thus, a mixture of backorders and lost sales exists. Derive two equations for finding simultaneously the best values of the order quantity (Q) and the maximum backorder quantity (b) that will minimize inventory costs. Use the following notation: D demand rate in units per year P production rate in units per year A = fixed cost of a replenishment order C unit variable cost of production the annual inventory carrying cost rate Q order quantity r =reorder point a backorder cost per unit short, independent of the duration of the shortage lost sales cost per unit short, independent of the duration of the shortage Q order quantity (decision variable) b maximum backorder level (decision variable)