Problem $20-31($Algo$)$

UA Hamburger Hamlet $($UAHH$)$ places a daily order for its high$-$volume items $($hamburger patties, buns, milk, and so on$).$ UAHH counts its current inventory on$-$hand once per day and phones in its order for delivery $24$ hours later.

Average daily demand $500$

Standard deviation of demand $90$

Desired service probability $95\%$

Hamburger inventory $865$

Determine the number of hamburgers UAHH should order for the above conditions: $($Use Excel's NORMSINV$()$ function to find the correct critical value for the given $\backslash$alpha $-$level. Do not round intermediate calculations. Round $"$z$"$ value to $2$ decimal places and final answer to the nearest whole number.$)$