Un problema de programación lineal resuelto por el método gráfico utilizando el lenguaje de programación R

programacionlineal.r

# Definir restricciones
restriccion.1 <- function(x) 30 - x  
# restriccion.2 x1 = 10 (Se dibuja usando geom_vline)
# restriccion.3 x2 = 10 (Se dibuja usando geom_vline)
# restriccion.4 x1 = 0 (Eje de abscisas)
# restriccion.4 x2 = 0 (Eje de ordenadas)
    
    # Importar ggplot2 paquete
library(ggplot2)

# Construir grafica
plano <- ggplot(data = data.frame(x = 0), aes(x = x)) +
  
  # Agregando ejes
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 0) +
  
  # Agregar lineas de restricciones
  stat_function(colour = "dodgerblue4", fun = restriccion.1, size = 1.5) +
  geom_vline(xintercept = 10, colour = "dodgerblue3", size = 1.5) +
  geom_hline(yintercept = 10, colour = "royalblue4", size = 1.5) +
  
  # Limites del grafico
  scale_x_continuous(breaks = seq(0, 100, 5), lim = c(0, 30)) +
  scale_y_continuous(breaks = seq(0, 100, 5), lim = c(0, 30)) +
  
  # Definir leyendas
  labs(title = "Programación Lineal",
       subtitle = "Método Gráfico",
       x = expression("x"[1]),
       y = expression("x"[2])) +
  
  # Fondo oscuro
  theme_dark()
    
  regionfactible = data.frame(x = c(10,10,20), y = c(10,20,10))

# Agregar region factible
plano <- plano + geom_polygon(data = regionfactible, mapping = aes(x = x, y = y), color = "slategray") +
  geom_point(data = regionfactible, aes(x = x, y = y), color = "Black", size = 2)


z1 <- function(x) -(3/2)*x + 10000/1000

    
plano <- plano + stat_function(colour = "yellowgreen", fun = z1, lty=2, size = 2)
    
z2 <- function(x) -(3/2)*x + 20000/1000

    
plano <- plano + stat_function(colour = "yellowgreen", fun = z2, lty=2, size = 2)
    

z3 <- function(x) -(3/2)*x + 30000/1000

    
plano <- plano + stat_function(colour = "yellowgreen", fun = z3, lty=2, size = 2)
    

z4 <- function(x) -(3/2)*x + 40000/1000

# punto de solucion
plano <- plano + stat_function(colour = "yellowgreen", fun = z4, lty=2, size = 2)
    
plano <- plano + geom_point(aes(x = 20, y = 10), color = "red", size = 4)

    
# Imprimir grafica
print(plano)


# Modificado de https://medium.com/swlh/operations-research-with-r-graphical-method-18f4ba34fea6