TStar buys two different types of chemical solvents $($Acetone and Formamide$)$ from the same

supplier. Acetone costs $$25$ per liter and Formamide costs $$48$ per liter. The ordering cost is $$65$

for Acetone and $$110$ for Formamide per order with a common cost of $$200.$ Holding costs are

based on a $30\%$ annual interest rate. The company uses an average of $18,000$ gallons per year

Acetone with a monthly standard deviation of $150$ gallons; and $24,000$ liters per year Formamide

with a monthly standard deviation of $230$ gallons. Lead time for order arrival is $6$ weeks and the

company would like to achieve $98\%$ customer service level for both solvents. $($assume $1$ year is $12$

months and $1$ month is $4$ weeks$)$

a$.$ Assuming that each solvent is independently ordered using periodic review. Calculate T$,$

M$,$ and the total annual cost of Acetone only. $(10$ points$)$

b$.$ Assuming that these solvents are jointly replenished, calculate the optimal inventory

replenishment interval, T$*,$ order$-$up$-$to levels, and the total annual cost. $(10$ points$)$