2. (15 points) A certain product is used up at an average rate of 300 units per day. The holding cost per unit inventory per day is $1, and the shortage cost per unit inventory is $5. The cost for placing an order is $60. Moreover, from historical record, the demand during lead time is uniform over the range (0,80) units. (i) Show that the optimal quantity to order, y*, exists and is unique. (ii) Write down the equations that the optimal (y*, R*) has to satisfy. (iii) Write down the algorithm initialization and the formulae for the iterates. (iv) Compute the optimal (y*, R*) to 2 decimal places. 2. (15 points) A certain product is used up at an average rate of 300 units per day. The holding cost per unit inventory per day is $1, and the shortage cost per unit inventory is $5. The cost for placing an order is $60. Moreover, from historical record, the demand during lead time is uniform over the range (0,80) units. (i) Show that the optimal quantity to order, y*, exists and is unique. (ii) Write down the equations that the optimal (y*, R*) has to satisfy. (iii) Write down the algorithm initialization and the formulae for the iterates. (iv) Compute the optimal (y*, R*) to 2 decimal places