Problem $1.$ Fresh connection $($a a fruit juices producer$)$ holds inventory of one of its

product: Fressie Orange $1$ liter in its warehouse. The current service level is set at $90\%.$

The warehouse replenished retail stores on a weekly basis so that the customer service

level could be defined as the probability of being in stock during the warehouse

replenishment lead time. The company wonders if this service level $(90\%)$ is proper. At

current service level, for each $1$ percent service level increase $($or decrease$),$ the sales

department estimates that it can increase $($or decrease$)$ sales by about $0\mathrm{.}15\%.$ The trading

margin $($markup$)$ is $$2$ per bottle with annual sales through the warehouse of $104,000$

bottles. The standard cost per bottle was $$3$ and the annual inventory carrying cost was

estimated at $30\%.$ The replenishment lead time is one week, with average weekly sales of

about $2000$ bottles and a standard deviation of $500$ bottles $($weekly$).$

If the company decides to increase the service level by $1\%,$ what is the change of z$-$score $($please only fill in the number, include $"-"$ sign if negative$)($keep $4$ decimal places$)?$

If the company decides to increase the service level by $1\%,$ what is the change of inventory cost $($only fill in the number, include $"-"$ sign if negative$)$

How much will the profit changes if this company decides to increase the service level by $1\%($please ONLY fill in the number include $-$ sign of if it is negative$)$