Problem C: Model a 2-D, confined aquifer under steady state conditions. Use a 8 x 8 grid representation with Delta_X = Delta_Y = 500 ft. Assume the transmissivity to be uniform at 12,500 ft^2/d, and a constant-head boundary condition at 39 ft at the upstream boundary, and 29.4 ft at the downstream boundary. In all scenarios the head at any location cannot be less than 23 ft. Assume no-flow conditions along the top and bottom boundaries. Potential pumping well sites are located at cells (3,3), (3,5), (3,7), (4,3), (4,5), (4,7), (5,3), (5,5), (5,7), (6,3), (6,5), and (6,7).

For some scenarios listed below, you may consider recharge wells, where the flow would be negative, to maintain head as required.

For each scenario, write out the mathematical model that was solved. Clearly label all variables. For each solution, report the value of each decision variable, the value of the objective function, and the value of each constraint.

Scenario 1. Suppose the right hand side boundary is close to a section of the aquifer with highly saline water. Using an LP model from Scenario 1, determine the pumping strategy that provides the maximum yield that could be achieved while ensuring that the saline water is prevented from entering the modeled area of the aquifer.

Scenario 2. Suppose the cell (2, 6) is suspected to contain toxic contamination. Using an LP model from Scenario 1, determine the pumping strategy that provides the maximum yield that could be achieved while ensuring that the toxic material is prevented from contaminating the cleaner section of the aquifer.