There are two pumping wells in the aquifer as shown in the Fig 23.3. Let us also consider that the main objective of the management model is to withdraw an amount of water equal to N_min. The finite difference form of the governing equation at each block centers has to be incorporated as constraints with the optimization problem along with the other constraints. Inclusion of these constraints ensures that the solution obtained would be physically feasible. The optimization problem can be formulated as,

Maximize

23.25

Subject to

	23.26
	23.27
	23.28
	23.29
	23.30
	23.31
	23.32
	23.33
	23.34
	23.35
	23.36
	23.37
	23.38

The constraint (23.36) ensures that the minimum withdrawn is N_min and the constraints (23.37) and (23.38) are the non negativity constraints. Here the decision variables are N₁ to N₁₀ and h₁ to h₁₀ are the state variables. The solution of the optimization problem will give spatial distribution of pumping pattern where total pumping from all the wells will be equal to N_min.