Consider the aquifer system shown below in plan and cross$-$sectional view. The well is $300m$ from a linear no$-$flow boundary and has a $1ft$ diameter. The aquifer parameters are uncertain and follow normal distributions with means $T=75,000$ gallons per day per foot and $S=0\mathrm{.}0001,$ and standard deviation for $T=5,000$ gallons per day per foot and for $S=0\mathrm{.}00002.$ The aquifer thickness is $10m$ and the static potentiometric surface is $15m$ above the bottom$-$confining layer. Find the maximum pumping rate $Q$ in liters$/$sec with which you can exploit this aquifer, such that the aquifer remains under pressure $($confined$)$ after $12$ hours of constant pumping, if you are willing to accept a level of reliability in your design of $99\mathrm{.}9\%,99\%,95\%,90\%$ and $80\%.$ Plot the Q vs$.$ reliability graph and comment on it$.$

Figure $2$: Plan and cross$-$section of pumping well