using for the 1st time the package

install.packages("linprog") 

#using the package
library(linprog)

#inserting parameters
cvec=c(40,100) 
bvec=c(20,12) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)

#solving our problem 
LP<-solveLP(cvec,bvec,A,maximum=T, const.dir=rep("<=", length(bvec)))
#Showing results
summary(LP) #print(LP)




#increase of A
cvec=c(40,100) 
bvec=c(21,12) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)
LP1<-solveLP(cvec,bvec,A,maximum=T, const.dir=rep("<=", length(bvec)))
#print(LP1)
summary(LP1) 

#shadow price
dx1 =7.5-6 
dx2 =1.5-2
shadow.price1=40*dx1+100*dx2 
shadow.price1


#decreasee of A
cvec=c(40,100) 
bvec= c(19,12) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)
LP2 =solveLP(cvec,bvec,A,maximum=T, const.dir=rep("<=", length(bvec)))
summary(LP2)

#shadow price
dx1 = 4.5-6 
dx2 = 2.5-2
shadow.price2=40*dx1+100*dx2 
shadow.price2

#increase of B
cvec=c(40,100) 
bvec=c(20,13) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)
LP3=solveLP(cvec,bvec,A,maximum=T, const.dir=rep("<=", length(bvec)))
summary(LP3)

#shadow price
dx1 = 4-6 
dx2 = 3-2
shadow.price3=40*dx1+100*dx2 
shadow.price3


#decrease of B
cvec=c(40,100) 
bvec=c(20,11) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)
LP4=solveLP(cvec,bvec,A,maximum=T, const.dir=rep("<=", length(bvec)))
summary(LP4)

#shadow price
dx1 = 8-6 
dx2 = 1-2
shadow.price4=40*dx1+100*dx2 
shadow.price4



#total results
results= rbind(c(440,6,2,"","initial LP"),c(450,7.5,1.5,10,"Increase 1st  constraint"),
               c(430,4.5,2.5,-10,"Decrease 1st constraint"),c(460,4,2,20,"Increase 2nd constraint"),
               c(420,8,1,-20,"Decrease 2nd constraint"))
results
Sensitivity=as.data.frame(results) 

Sensitivity

names(Sensitivity) = c("Value of Objective Function",
                        "Quantity of X1","Quantity of X2","shadow price","Change of constraint") 
Sensitivity


#instaalling and using the package
install.packages("lpSolve") 
library(lpSolve)


#inserting parameters
cvec=c(40,100) ; bvec=c(20,12) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)

#always insert the direction for each one constraint 
constr.dir=c("<=","<=")

#counting the value of O.F.
LP5 = lp("max",cvec, A, constr.dir, bvec,compute.sens=0); LP5
#or
lp("max",cvec,A,constr.dir,bvec,compute.sens=0)$objval

#successful or no? (0 Επιτυχής εκτέλεση του αλγορίθμου/ 1,2,3,4,5 ΝΟ)
lp("max",cvec,A,constr.dir,bvec)$status

#showing the quantities of x1,x2
lp("max", cvec, A, constr.dir, bvec)$solution 

#showing shadow prices
lp("max",cvec,A,constr.dir,bvec,compute.sens=1)$duals



#changing positions of arguments inside the command
lp("max",bvec, A, constr.dir,cvec)
lp("max",bvec, A, constr.dir,cvec)$solution

lp("max",A,cvec,constr.dir,bvec)
lp("max",A,cvec,constr.dir,bvec)$solution


#using lpSolve through linprog
library(linprog)
cvec=c(40,100) ; bvec=c(20,12) 
A=matrix(c(2,4,1,3),nrow=2,ncol=2,byrow=T)
LP6=solveLP(cvec,bvec,A,maximum=T,const.dir=c("<=","<="), lpSolve = T)
summary(LP6)

#shadow prices
LP7 =solveLP(cvec,bvec,A,maximum=T,const.dir=c("<=","<="), lpSolve = T, solve.dual = T)
print(LP7)