#Tengo 4 cargas, todas pueden ser distribuidas en delantero , central o trasero. 
#XiD : toneladas de la carga i en el delantero
#XiC: toneladas de la carga i en el central
#XiR: toneladas de la carga i en el trasero
#i=1,2,3,4

#Objetivo = maximizar ganancias 
#MAX 320X1D+320X1C+320X1T+ 400X2D+400X2C+400X2T+360X3D+360X3C+360X3T+290X4D+290X4C+290X4T

obj<-c(320,320,320,400,400,400,360,360,360,290,290,290)

#Capacidad de carga en compartimientos D,C,T

#1)X1D+X2D+X3D+X4D<12
#2)X1C+X2C+X3C+X4C<18
#3)X1T+X2T+X3T+X4T<10

#Capacidad de cargas i 
#4)X1D+X1C+X1T<20
#5)X2D+X2C+X2T<16
#6)X3D+X3C+X3T<25
#7)X4D+X4C+X4T<13

#Relación volumen con capacidad 
#8)500X1D+700X2D+600X3D+400X4D<7000
#9)500X1C+700X2C+600X3C+400X4C<9000
#10)500X1T+700X2T+600X3T+400X4T<5000

# "proporción de la capacidad en cada compartimiento"
#11) XD/12 - XC/18=0
#12) XD/12-XC/10=0
#11)0.0833X1D+0.0833X2D+0.0833X3D+0.0833X4D-0.05556X1C-0.05556X2C-0.05556X3C-0.05556X4C=0
#12)0.0833X1D+0.0833X2D+0.0833X3D+0.0833X4D-0.1X1T-0.1X2T-0.1X3-0.1X4T=0

#Matriz de restricciones 13x12

A<-matrix(ncol=12,nrow=13)

A[1,]<-c(1,0,0,1,0,0,1,0,0,1,0,0)
A[2,]<-c(0,1,0,0,1,0,0,1,0,0,1,0)
A[3,]<-c(0,0,1,0,0,1,0,0,1,0,0,1)
A[4,]<-c(1,1,1,0,0,0,0,0,0,0,0,0)
A[5,]<-c(0,0,0,1,1,1,0,0,0,0,0,0)
A[6,]<-c(0,0,0,0,0,0,1,1,1,0,0,0)
A[7,]<-c(0,0,0,0,0,0,0,0,0,1,1,1)
A[8,]<-c(500,0,0,700,0,0,600,0,0,400,0,0)
A[9,]<-c(0,500,0,0,700,0,0,600,0,0,400,0)
A[10,]<-c(0,0,500,0,0,700,0,0,600,0,0,400)
A[11,]<-c(0.7,-0.3,-0.3,0.7,-0.3,-0.3,0.7,-0.3,-0.3,0.7,-0.3,-0.3)
A[12,]<-c(-0.45,0.55,-0.45,-0.45,0.55,-0.45,-0.45,0.55,-0.45,-0.45,0.55,-0.45)
A[13,]<-c(-0.25,-0.25,0.75,-0.25,-0.25,0.75,-0.25,-0.25,0.75,-0.25,-0.25,0.75)



print(A)

#Vector de direcciones
dir<-c("<","<","<","<","<","<","<","<","<","<","=","=","=")

#Vectores de valores de la derecha
rhs<-c(12,18,10,20,16,25,13,7000,9000,5000,0,0,0)

#LpSolve

library(lpSolve)

SOLUCION<-lp(direction = "max",objective.in = obj,const.mat = A,const.dir = dir,const.rhs = rhs)
print(SOLUCION)

Cargas<-SOLUCION$solution
print(Cargas)

#Analisis de soluciones 

#GANANCIA TOTAL= 13 330 
#X1D=0
#X1C=14.67
#X1T=0
#X2D=7.33
#X2C=0
#X2T=3.33
#X3D=0
#X3C=1.67
#X3T=0
#X4D=4.67
#X4C=1.67
#X4T=6.67

#X1=14.67 / X2=10.67 / X3=1.67 / x4=13
#XD=12 / XC=18 / XT=10