I need starting the Matlab programming

My friend Matt used to live in a house that sits on a hillside. His up$-$slope neighbor had $6,400m^2$ of beautifully manicured lawn, which required a large volume of water to sustain. My friend and his neighbor each had water supply wells on their respective properties tapping the same confined aquifer.

You are tasked with finding $(A)$ if the pumping rate employed by the up$-$slope neighbor will allow Matt's well to continue operation, and $($B$)$ what the maximum pumping rate the up$-$slope neighbor may use while still allowing Matt's well to provide sufficient water for his family.

Represent the hillside aquifer by a $5050$ grid.

Each grid space should be a square $1010$ m$.$

The top and bottom of the hill should be represented by constant$-$head $($Dirichlet$)$ boundary conditions, $404$ m at the top, $383$ at the bottom.

The sides of the model domain should be represented by no$-$flow $($Neumann$)$ bounda conditions.

Here are a few facts:

Resources of the Fairfax Quadrangle

Matt's family uses $248$ gallons of water per day.

The neighbor is currently pumping $1252$ gallons per day.

Both wells have a diameter of $15$ cm $.$

The neighbor's lawn is $8080m,$ and its lower left corner is located $200$ m from the left side of the hillslope, and $400$ m from the bottom.

The neighbor's well is located $285$ m from the left, and $405$ m from the bottom.

Matt's well is located $235$ m from the left, and $215$ m from the bottom.

The head in Matt's well cannot drop below $197$ m $.$

$*2\%$ of the water pumped by the neighbor re$-$infiltrates the aquifer. This re$-$infiltration is distributed over the $64$ grid cells containing the lawn.

The aquifer is $20$ m thick.

You will be provided with Saturated Hydraulic Conductivity $(K_{\text{s}\text{a}\text{t}})$ values in units of $\frac{m}{?}$ day and initial hydraulic head values in units of meters for every grid square.

The main equation you will use is Darcy's Law,

$q=-K_{\text{s}\text{a}\text{t}}$gradh$+\frac{Q_{io}}{A}$

where q is the flow rate $($Darcy velocity$),$ gradh is the head gradient, and $Q_{io}$ is water added or removed by means other than groundwater flow $($i$.$e$.$ well pumping, infiltration$).$

Represent the head gradient using a forward finite difference method. Solve the system of equations that represent flow into and out of each grid cell using the Gauss$-$Seidel method. Find a maximum by interpolating a few data points or using a least$-$squares fit, and maximizing the resulting function.

Deliverable

Please provide a report describing your work and your results. Your report should contain the following sections:

Introduction: explain the problem and the purpose of the project, and summarize the outcome.

Methods: explain what you did $-$ what techniques you used, why you used them, and how they work. Concentrate on the mathematical methods. That's what's really important here. MATLAB programming and hydrology should be only a small part of this section. This is the most important section of the

report. It should include the following: