A puzzle store, Dorogi's Wizard Wheezes, has different variety of brainteasers and jigsaw puzzles. One particular puzzle, Impossible, sells for $25 each, and it costs $15 to purchase it from a designer. There is a $50 replenishment cost per order. A backorder results in the loss-of-goodwill with estimated cost $40 per puzzle. You can assume the unmet demand is backlogged. There is a 2-month lead time and an inventory carrying charge of 15 % annual interest rate. The monthly demand for Impossible puzzle follows a normal distribution with mean 300 and standard deviation 65.

(a) (4 points) What is the value of Q0, if Q0 is estimated using the EOQ model?

(b) (4 points) What is the value of R0?

(c) (4 points) What are the values of Q1 and R1?

(d) (10 points) Currently Dorogi's uses the reorder point of 20 units and the lot size of 100 units. A manager from the new generation of puzzle masters, Natalia, plans to increase the lot size from 100 units to 120 units. Then, does the probability of not stocking out during the lead time increase or decrease? How about the proportion of demand that is met from on-hand stock? Explain your reasoning clearly either with math or in words.