Problem $3.$

$2.(26$ points$)$ A puzzle store, Wang's Wizard Wheezes $($WWW$),$ has different varieties of brain$-$teasers and jigsaw puzzles. One particular puzzle, Impossible, sells for $$25$ each,and it costs $$15$ to purchase it from a designer. There is a $$50$ replenishment cost per order. A backorder results in the loss$-$of$-$goodwill with an estimated cost of $$40$ per puzzle. You can assume the unmet demand is backlogged. There is a $3-$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 $81.$ Justice Shelton,CEO of WWW$,$uses $($Q$,$R$)$ policy for ordering inventory.

a$)$ Find RO$?$

b$)$ Find Q$1$ and R$1?$