#install.packages(linprog)
#install.packages(lpSolve)


#using linprog
library(linprog)
cvec = c(15000,9500) ; bvec = c(960,400, 420) 
A =  matrix(c(8,8,4,2,4,3), nrow=3, ncol=2, byrow=T)
LP = solveLP(cvec,bvec,A,maximum=T) ; print(LP)


#using lpSolve
library(linprog); library(lpSolve)
cvec = c(15000,9500) ; bvec = c(960,400, 420) 
A =  matrix(c(8,8,4,2,4,3), nrow=3, ncol=2, byrow=T)
LP1 = solveLP(cvec, bvec, A, maximum = T, const.dir =c("<=","<=","<="),
              lpSolve = T, solve.dual = T) 
print(LP1)


#duality
cvec = c(15000,9500) ; bvec = c(960,400, 420) 
A =  matrix(c(8,8,4,2,4,3), nrow=3, ncol=2, byrow=T)
primal = solveLP(cvec,bvec,A,maximum=T, lpSolve=T,
                 solve.dual=T) ; print(primal)


cvec = c(960,400, 420) ; bvec = c(15000,9500) 
A =  matrix(c(8,4,4,8,2,3), nrow=2, ncol=3, byrow=T)
dual = solveLP(cvec,bvec,A,maximum=F, const.dir=c(">=",">="),
               lpSolve=T, solve.dual=T) ; print(dual)


#2nd example

cvec = c(1,1) ; bvec = c(150)  
A = matrix(c(2,1), nrow=1, ncol=2, byrow=T)
utility_max = solveLP(cvec,bvec,A,maximum=T, lpSolve=T,
                      solve.dual=T) ; print(utility_max)

cvec = c(150) ; bvec = c(1,1) 
A =matrix(c(2,1),nrow=2,ncol=1,byrow=T)
expenditure_min = solveLP(cvec,bvec,A,maximum=F,
                          const.dir=c(">=",">="), lpSolve=T, solve.dual=T) ;
print(expenditure_min)