[SOLVED] I'm trying to get the positive solutions to the following system of linear equations

I'm trying to get the positive solutions to the following system of linear equations

5.1x + 15y +z = 280
6.9x + 17y +z = 320
5.3x + 13y +z = 270

I am particularly interested in solutions where x >= 30 I have done the following but I would like to get the other solutions

 A <- rbind(c(5.1, 15, 1),  
           c(6.9, 17, 1),  
           c(5.3, 13, 1)) 
 B <- c(280, 320, 270) 
 solve(A, B)

Solution

You have no opportunity to control the solution once you have a unique solution since A is full rank.

However, if you remove the last equation from your system, say, AA <- A[-3, ] and BB <- B[-3], then AA becomes rank deficient, and you will have room to add the constraint x>=30 to achieve one solution.

For example, given AA and BB like below

AA <- A[-3, ]
BB <- B[-3]

we can make a random x>=30 like aux <- 30 + abs(rnorm(1))., and solve the problem

> solve(rbind(AA, c(1, rep(0, ncol(AA) - 1))), c(BB, aux))
[1]  30.787640  -7.708876 238.616173