6. A certain product is used up at an average rate of 500 units per day. The holding cost per unit inventory per day is $1, and the shortage cost per unit inventory is $10. The cost for placing an order is $20. Moreover, from historical record, the demand during lead time is uniform over the range (0,50) units. Show that the optimal quantity to order, y*, exists and is unique; write down the equations that the optimal (y*, R*) has to satisfy; write down the algorithm initialization and the formulae for the iterates; you do NOT need to compute the optimal (y*, R*).