The annual demand for a specific product is 3,500 units and has the following ordering and holding costs: C_o = $20.50 per order and C_h = $8.00 per unit. Demand exhibits some variability such that the lead-time demand follows a normal probability distribution with = 45 units and = 12 units.

a) What is the recommended order quantity for this product? Express your answer as a whole number using standard rounding rules.

b) If the manager sets the reorder point at 55 units, what is the probability of a stockout in any given order cycle? Express your answer as a decimal to 4 decimal places using standard rounding rules.

c) Given the probability of a stockout in problem b, how many times would expect a stockout to occur during the year if the reorder point = 55 units were used? Express your answer to 2 decimal places using standard rounding rules.

*Please explain how to calculate*