This problem represents a steady$-$state dewatering problem for a construction site. The objective of the

ground$-$water management problem is to minimize the cost of withdrawing groundwater to lower heads

to an elevation of $18m,$ so that footings can be installed in the area shown in Figure $3.$ Wells at the

construction site are located as shown and can be assumed to be at the centroid of the cell. The wells will

be pumped for $180$ days in order to complete the construction of the foundation. The aquifer at the site is

horizontal and confined with a thickness of $15m$ and is $2500m$ long and $1000m$ wide. The upper

confining layer is $3m$ thick and is $2m$ below the ground surface. It cannot be considered totally

impermeable once it is exposed during the excavation. The model grid consists of $20$ rows and $50$

columns, and each grid cell is $50m$ by $50m.$ Based on the hydrogeologic conditions of the site, the

model can employ no$-$flow boundary conditions along the north and south boundaries of the aquifer and

constant heads of $30m$ and $20m$ along the west and east boundaries of the aquifer, respectively. The

average transmissivity of the aquifer is $10\frac{m^2}{d}.$ The radius of influence of all wells is $400m.$

a$)$ Find the minimum flowrate that all wells should be pumped at in order to ensure that no part of

the excavation is under water.

b$)$ Repeat but allow wells to have different flowrates $($maximum of $3$ different values$).$

Figure $3$: Schematic of the confined aquifer and construction zone