Determining Optimum Service Levels $($Cont$\text{'}$d$)$

Sales response rate is $0\mathrm{.}1\%$ change in revenue for a $1\%$ change in the service level $($fill rate$).$ Trading margin is $$4$ per item, inventory carrying cost is $24\%$ per year, annual sales through the warehouse is $100,000$ items. Cost of each item is $$30,$ demand standard deviation is $690$ items for a week, and the lead time is $3$ weeks. Given the above data for a particular product calculate

a$)z$

b$)$ Optimal CSL