Update docs

Author: scheinerman

README.md

@@ -1,20 +1,35 @@
 # SimpleTableaux
 
-Solve linear programming problems using the simplex method by pivoting
+This module can be used to show how to solve linear programming problems using the simplex method by pivoting
 tableaux. 
 
 This is an illusration project for solving 
 feasible optimization problems of the form 
-$\max c^t x$ subject to $Ax ≤ b$ and $x \ge 0$.
+$\max c^t x$ subject to $Ax ≤ b$ and $x \ge 0$. 
 
-Here are some quick start instructions. 
+## Caveats
+
+As a demonstration project, this is not suitable for solving actual linear programming (LP) problems. 
+At present it will fail if:
+* The LP is infeasible.
+* The LP is unbounded.
+* Other unidentified reasons.
+
+It is also set up for maximization problems only. To solve a minimization problem use the dual LP by
+replacing the inputs `A`, `b`, and `c` with `A'`, `c`, and `b` respectively. 
+
+
+
+
+# Quick Start Instructions
 
 ## Set up the problem
 
 This example comes from [this video](https://www.youtube.com/watch?v=rzRZLGD_aeE).
 
 Create the matrix `A`, the RHS vector `b`, and the objective function coefficients `c`:
 ```
+julia> using SimpleTableaux
 julia> A = [3 5; 4 1];
 julia> b = [78; 36];
 julia> c = [5; 4];
@@ -36,7 +51,6 @@ Notice that the last row is the encoding of the objective function.
 
 ```
 julia> x = pivot_solve(T)
-Iteration 0
 3×6 DataFrame
  Row │ x1     x2     s1     s2     val    RHS   
      │ Exact  Exact  Exact  Exact  Exact  Exact 
@@ -45,7 +59,9 @@ Iteration 0
    2 │ 4      1      0      1      0      36
    3 │ -5     -4     0      0      1      0
 
-Iteration 1
+
+Pivot at (2,1)
+
 3×6 DataFrame
  Row │ x1     x2     s1     s2     val    RHS   
      │ Exact  Exact  Exact  Exact  Exact  Exact 
@@ -54,7 +70,9 @@ Iteration 1
    2 │ 1      1/4    0      1/4    0      9
    3 │ 0      -11/4  0      5/4    1      45
 
-Iteration 2
+
+Pivot at (1,2)
+
 3×6 DataFrame
  Row │ x1     x2     s1     s2     val    RHS   
      │ Exact  Exact  Exact  Exact  Exact  Exact 
@@ -63,7 +81,7 @@ Iteration 2
    2 │ 1      0      -1/17  5/17   0      6
    3 │ 0      0      11/17  13/17  1      78
 
-Optimum value = 78
+Optimum value after 2 iterations = 78
 2-element Vector{Rational{BigInt}}:
   6
  12
@@ -86,11 +104,13 @@ julia> c' * x == 78
 true
 ```
 
-## Repeat using an LP solver (HiGHS)
+## Repeat using a proper LP solver
 
 ```
 julia> lp_solve(T)
 2-element Vector{Float64}:
   6.0
  12.0
-```
+```
+
+The `lp_solve` function uses the [HiGHS](https://highs.dev/) solver.