Continuing their $$thinking outside$-$the$-$box,$$ the management team is now asking you to calculate the

inventory control implications of developing a single engine oil product that they can sell for all types of

engines $-$diesel, gas and natural gas. That is$,$ this single product will be a substitute for all of the three

products, and in fact, will have superior properties in reducing friction $($thanks to the addition of boric acid

to the formulation$),$ and will eventually take over market share of the other products. The marketing team

thinks that there will be a transitionary period during which the company will also be selling the previous

three fuel$-$specific products, but within a year or so they expect the new engine oil to wipe out the other

products off the market. Alex Hamm is particularly interested in demonstrating the inventory control

impacts of this idea in the long$-$run, since he has learned in his Operations Management class that

standardizing inventories would yield risk pooling benefits. He has asked for your help in calculating the

optimal $($Q$,$R$)$ policy and its costs and performance $($fill rate and stock$-$out probability$)$ in this case. How does

the performance of this policy compare to that of the policy you calculated for Part $(2),$ for three different

engine oil products?