simplex algorithm

simplex algorithm
请问是否有一个叫做The Simplex Algorithm的算法.
可否介绍一个算法跟The Simplex Algorithm类似的算法,用c或者c++实现.
或者第二个问题：
Consider the linear programming problem with constraints x ≥ 0 and
x1 +4x2 −2x3 +4x4 +3x5 +3x6 −2x7 −x8 ≤ 2
x1 +4x2 +5x3 +6x4 +x5 −2x6 +4x7 ≤ 3
3x1 +6x2 −2x4 +2x5 −3x6 −2x7 +5x8 ≤ 5
−x1 +2x2 −x3 +5x5 +x6 +3x7 +4x8 ≤ 3
5x1 −x2 +4x3 −x4 −3x7 −2x8 ≤ 2.
Use your program to maximize each of the following objective functions:
f1(x) = x1 + 3x2 − 3x5 + x6 − x7
f2(x) = 2x1 + x2 − x3 + 2x4 − 3x5 + x6 + 3x7 + x8
f3(x) = x1 + 3x2 − x3 + x4 − 3x6 + x7 + 2x8.
Give the optimal value of x in each case.
Investigate the number of iterations required,if (i) we choose the variable to enter the
basis at random,or (ii) we always take a0j maximal.