library(lpSolve)
#Defino variables del problema
#xi: cantidad de tableros del tipo i producidos
#zi: cantidad de tableros del tipo i comprados
#i=a,b,c,d 

#Restricciones de especificación

#E) 0.05xa+ 0.05xb+ 0.05xc+ 0.05xd <= 1200
#AR) 0.1Xa + 0.12Xb + 0.14xc + 0.18xd <= 3600
#C) 0.2xa + 0.25xb + 0.3xc + 0.25xd <= 5000
#AJ) (0.8/9)xa + (1/9)xb + (0.6/9)xc + (1/9)xd <= 3000
#CCprod y compra) (0.2/9)xa + (0.3/9)xb + (0.3/9)xc + (0.3/9)xd + 0.03za + 0.05zb
#  + 0.04zc + 0.04zd <= 3000

#Restricciones de balance

# xa + za = 4000
# xb + zb = 3000
# xc + zc = 8000
# xd + zd = 5000

coef<-c(500,600,1200,1000,600,750,1800,800)
A<-matrix(c(0.05,0.05,0.05,0.05,0,0,0,0,
            0.1,0.12,0.14,0.18,0,0,0,0,
            0.2,0.25,0.3,0.25,0,0,0,0,
            0.8/9,1/9,0.6/9,1/9,0,0,0,0,
            0.2/9,0.3/9,0.3/9,0.3/9,0.03,0.05,0.04,0.04,
            1,0,0,0,0.8,0,0,0,
            0,1,0,0,0,0.8,0,0,
            0,0,1,0,0,0,0.8,0,
            0,0,0,1,0,0,0,0.8),ncol=8,nrow=9,byrow=TRUE)

b<-c(1200,3600,5000,3000,3000,4000,3000,8000,5000)
dir<-c(rep('<=',5),rep("=",4))

valobj <- lp('min', coef, A, dir, b)
print(A)
print(valobj)
solvar <- lp('min', coef, A, dir, b)$solution
print(solvar)