install.packages("lpSolve")

library("lpSolve")

# Sean las variables como:
# XPi= cantidad de piezas i producidas
# i:A, B, C, D

# XCj= cantidad de piezas i compradas
# i: A, B, C, D

# Restricciones
# 0.05XPa + 0.05XPb + 0.05XPc + 0.05XPd <= 1200
# 0.1XPa + 0.12XPb + 0.14XPc + 0.18XPd <= 3600
# 0.2XPa + 0.25XPb + 0.3XPc + 0.25XPd <= 5000
# 0.088XPa + 0.11XPb + 0.066XPc + 0.11XPd <= 3000
# 0.088XPa + 0.11XPb + 0.066XPc + 0.11XPd + 0.0375XCa + 0.0625XCb
#   + 0.05XCc + 0.05XCd <= 3000
# XPa + XCa = 4000
# XPb + XCb = 3000
# XPc + XCc = 8000
# XPd + XCd = 5000

# MAX: 500XPa + 600XPb + 1200XPc + 1000XPd - 800XCa - 750XCb - 1800XCc - 800XCd

Z <- c(500,600,1200,1000,-800,-750,-1800,-800)
Restric <- 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,
                    0.088,0.11,0.066,0.11,0,0,0,0,
                    0.088,0.11,0.066,0.11,0.0375,0.0625,0.05,0.05,
                    1,0,0,0,1,0,0,0,
                    0,1,0,0,0,1,0,0,
                    0,0,1,0,0,0,1,0,
                    0,0,0,1,0,0,0,1), nrow=9, byrow=TRUE)
Signos <- c("<=","<=","<=","<=","<=","=","=","=","=")
RHS <- c(1200,3600,5000,3000,3000,4000,3000,8000,5000)

lpSolve::lp("max", Z, Restric, Signos, RHS)

lpSolve::lp("max", Z, Restric, Signos, RHS)$solution