a$)$ Suppose that in the above problem the stock$-$out cost is replaced with a Type $1$ service

objective of $95$ percent. Find the optimal values of $($Q$,$ R$)$ in this case.b$)$

b$)$ Suppose that in problem $13$ a Type $2$ service objective of $95$ percent is substituted for the

stock$-$out cost of $$12\mathrm{.}80.$ Find the resulting values of Q and R$.$ Also, what is the imputed cost

of shortage for this case?

c$)$ Suppose that the warehouse from problem $13$ mistakenly used a Type $1$ service objective when

it really meant to use a Type $2$ service objective $($see problems a and b$).$ What is the additional

holding cost incurred each year for this item because of this mistake?