$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multicolumn$\{11\}\{|$c$|\}\{$Mean$\}\backslash \backslash$

$\backslash$hline & $\backslash$multicolumn$\{2\}\{|$c$|\}\{2\mathrm{.}2\}$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{2\mathrm{.}4\}$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{2\mathrm{.}6\}$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{2\mathrm{.}8\}$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{3\mathrm{.}0\}\backslash \backslash$

$\backslash$hline $\backslash ($ s $\backslash )$ & F$($S$)$ & I$($S$)$ & F$($s$)$ & I$($S$)$ & F$($s$)$ & I$($S$)$ & F$($S$)$ & I$($S$)$ & F$($S$)$ & I$($S$)\backslash \backslash$

$\backslash$hline $0$ & $0\mathrm{.}1108$ & $0\mathrm{.}00$ & $0\mathrm{.}0907$ & $0\mathrm{.}00$ & $0\mathrm{.}0743$ & $0\mathrm{.}00$ & $0\mathrm{.}0608$ & $0\mathrm{.}00$ & $0\mathrm{.}0498$ & $0\mathrm{.}00\backslash \backslash$

$\backslash$hline $1$ & $0\mathrm{.}3546$ & $0\mathrm{.}11$ & $0\mathrm{.}3084$ & $0\mathrm{.}09$ & $0\mathrm{.}2674$ & $0\mathrm{.}07$ & $0\mathrm{.}2311$ & $0\mathrm{.}06$ & $0\mathrm{.}1991$ & $0\mathrm{.}05\backslash \backslash$

$\backslash$hline $2$ & $0\mathrm{.}6227$ & $0\mathrm{.}47$ & $0\mathrm{.}5697$ & $0\mathrm{.}40$ & $0\mathrm{.}5184$ & $0\mathrm{.}34$ & $0\mathrm{.}4695$ & $0\mathrm{.}29$ & $0\mathrm{.}4232$ & $0\mathrm{.}25\backslash \backslash$

$\backslash$hline $3$ & $0\mathrm{.}8194$ & $1\mathrm{.}09$ & $0\mathrm{.}7787$ & $0\mathrm{.}97$ & $0\mathrm{.}7360$ & $0\mathrm{.}86$ & $0\mathrm{.}6919$ & $0\mathrm{.}76$ & $0\mathrm{.}6472$ & $0\mathrm{.}67\backslash \backslash$

$\backslash$hline $4$ & $0\mathrm{.}9275$ & $1\mathrm{.}91$ & $0\mathrm{.}9041$ & $1\mathrm{.}75$ & $0\mathrm{.}8774$ & $1\mathrm{.}60$ & $0\mathrm{.}8477$ & $1\mathrm{.}45$ & $0\mathrm{.}8153$ & $1\mathrm{.}32\backslash \backslash$

$\backslash$hline $5$ & $0\mathrm{.}9751$ & $2\mathrm{.}83$ & $0\mathrm{.}9643$ & $2\mathrm{.}65$ & $0\mathrm{.}9510$ & $2\mathrm{.}47$ & $0\mathrm{.}9349$ & $2\mathrm{.}30$ & $0\mathrm{.}9161$ & $2\mathrm{.}13\backslash \backslash$

$\backslash$hline $6$ & $0\mathrm{.}9925$ & $3\mathrm{.}81$ & $0\mathrm{.}9884$ & $3\mathrm{.}62$ & $0\mathrm{.}9828$ & $3\mathrm{.}42$ & $0\mathrm{.}9756$ & $3\mathrm{.}24$ & $0\mathrm{.}9665$ & $3\mathrm{.}05\backslash \backslash$

$\backslash$hline $7$ & $0\mathrm{.}9980$ & $4\mathrm{.}80$ & $0\mathrm{.}9967$ & $4\mathrm{.}60$ & $0\mathrm{.}9947$ & $4\mathrm{.}41$ & $0\mathrm{.}9919$ & $4\mathrm{.}21$ & $0\mathrm{.}9881$ & $4\mathrm{.}02\backslash \backslash$

$\backslash$hline $8$ & $0\mathrm{.}9995$ & $5\mathrm{.}80$ & $0\mathrm{.}9991$ & $5\mathrm{.}60$ & $0\mathrm{.}9985$ & $5\mathrm{.}40$ & $0\mathrm{.}9976$ & $5\mathrm{.}20$ & $0\mathrm{.}9962$ & $5\mathrm{.}01\backslash \backslash$

$\backslash$hline $9$ & $0\mathrm{.}9999$ & $6\mathrm{.}80$ & $0\mathrm{.}9998$ & $6\mathrm{.}60$ & $0\mathrm{.}9996$ & $6\mathrm{.}40$ & $0\mathrm{.}9993$ & $6\mathrm{.}20$ & $0\mathrm{.}9989$ & $6\mathrm{.}00\backslash \backslash$

$\backslash$hline $10$ & $1\mathrm{.}0000$ & $7\mathrm{.}80$ & $1\mathrm{.}0000$ & $7\mathrm{.}60$ & $0\mathrm{.}9999$ & $7\mathrm{.}40$ & $0\mathrm{.}9998$ & $7\mathrm{.}20$ & $0\mathrm{.}9997$ & $7\mathrm{.}00\backslash \backslash$

$\backslash$hline $11$ & $1\mathrm{.}0000$ & $8\mathrm{.}80$ & $1\mathrm{.}0000$ & $8\mathrm{.}60$ & $1\mathrm{.}0000$ & $8\mathrm{.}40$ & $1\mathrm{.}0000$ & $8\mathrm{.}20$ & $0\mathrm{.}9999$ & $8\mathrm{.}00\backslash \backslash$

$\backslash$hline $12$ & $1\mathrm{.}0000$ & $9\mathrm{.}80$ & $1\mathrm{.}0000$ & $9\mathrm{.}60$ & $1\mathrm{.}0000$ & $9\mathrm{.}40$ & $1\mathrm{.}0000$ & $9\mathrm{.}20$ & $1\mathrm{.}0000$ & $9\mathrm{.}00\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$ Demand for a product follows the Poisson distribution with a mean of $0\mathrm{.}6.$ If the lead time is $2$ periods and the order up to level is $5.$

Use Table $14$A$.2.$

What is the expected on$-$hand inventory?

Note: Round your answer to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places. Demand each period for a product is normally distributed $($mean $\backslash (=725\backslash ),$ standard deviation $\backslash (=145\backslash )).$ The lead time is $4$ periods.

What is the minimum order$-$up$-$to level to ensure an in$-$stock probability of $0\mathrm{.}90?$

Note: Round your answer to the nearest whole number. Demand for a product follows the Poisson distribution with a mean of $0\mathrm{.}6.$ If the lead time is $2.$ Use Table $14$A$\mathrm{.}2.$

What is the minimum order$-$up$-$to level to ensure an in$-$stock probability of $0\mathrm{.}93?$