线性编程（lpsolve）在向函数添加常量时提供不同的解决方案

Question

我显然在这里做错了什么，但我无法理解。我有一个函数矩阵来最大化调用这里的排名（如果感兴趣的是男性和女性交配的预期后代表现）与一些约束 - 一切功能价值都是积极的。我运行它并获得解决方案。然后我为所有函数值添加一个常量（这里是10），我得到了一个不同的解决方案。我不是LP专家，但这没有任何意义 - 确定为一切添加一个常数不应该改变事情吗？

library(lpSolve)
rank <- matrix(c(1, 2, 3, 4, 5,6, 7, 8), nrow=2, ncol=4,byrow=T)
rank<- rank+10  # switch on and off
rank
exclusions<-  matrix(c(0,0,0,0,0,0,0,0), nrow=2, ncol=4,byrow=T)
sires <- matrix(c(2,2), nrow=1, ncol=2,byrow=T)
m <- NROW(rank) # n of males
f <- NCOL(rank) # n of females
obj <- as.numeric(rank)    # objective function
nMalePerFemaleRhs <- rep(1,f)    # one mating per female 
nMalePerFemaleSign <- rep("<=",f)   # every female must gets no more than 1 mating 
nMalePerFemaleConstr <- matrix(0,nrow=f,ncol=m*f)

for(i in 1:f){
  nMalePerFemaleConstr[i,(i-1)*m+(1:m)] <- 1    # cows are rows and the number of columns are bulls times cows
}

nFemalePerMaleRhs <- sires[1,] # number of matings per sire
nFemalePerMaleSign <- rep("<=",m)  
nFemalePerMaleConstr <- matrix(0,nrow=m,ncol=m*f)

for(i in 1:m){
  nFemalePerMaleConstr[i,seq(from=i,length.out=f,by=m)] <- 1
}


######################################################
#         Sibling exclusions constraint              #
######################################################

siblingConstr <- t(as.numeric(exclusions))
siblingRhs <- 0
siblingSign <- '='


######################################################
#           Solve the linear program                 #
######################################################

res <- lp(direction='max',
          objective.in=obj,
          const.mat = rbind
(nMalePerFemaleConstr,nFemalePerMaleConstr,siblingConstr),
          const.dir = c(nMalePerFemaleSign,nFemalePerMaleSign,siblingSign),
          const.rhs = c(nMalePerFemaleRhs,nFemalePerMaleRhs,siblingRhs),
          all.int = TRUE
          )

solutionLP <- matrix(res$solution,nrow=m)

solutionLP