I have a set of linear equations and would like to find any feasible solution.
A simplex solution works in Case 1 below, but not in Case 2. I would be
grateful for any help.
Case 1: Find any feasible solution for the set of linear equations:
a + b + c = 5
a + b + 0c = 4
0a + b + c = 4
Solution - a feasible (and unique) solution is a=1, b=3, c=1.
The following R code returns a feasible solution:
A3M = matrix(c(1,1,0,1,1,1,1,0,1),nrow=3)
b3M = matrix(c(5,4,4),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 = b3M,
maxi = TRUE)
Case 2: Find any feasible solution for the set of linear equations
a + b + c = 5
a + 0b + c = 2
0a + b + 0c = 3
Solution - one feasible solution of many is a=1, b=3, c=1. There are infinite
possible solutions in Case 2.
However, the following R code fails to return any feasible solution:
A3M = matrix(c(1,1,0,1,0,1,1,1,0),nrow=3)
b3M = matrix(c(5,2,3),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 = b3M,
maxi = TRUE)
The code returns the error:
Error in A.out[, basic] <- iden(M) : subscript out of bounds
Am I using the Simplex function incorrectly? There may be a better way to
approach the problem of finding a feasible solution.
Cheers,
Chris.
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