Linear Programming for Soda company

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import library

library(lpSolve)

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Objective Function

• Max(13X₁ + 23X₂ + 30X₃)

Subject to (Constraints)

• 5X₁ + 15X₂ + 4X₃ <= 480 (CO2)
• 4X₁ + 4X₂ + 10X₃ <= 160 (Water)
• 35X₁ + 20X₂ + 15X₃ <= 1190 (Flavor)
• 5X₁ + 10X₂ + 20X₃ <= 200 (number of worker * work hours * 5 days)
• X₁, X₂, X₃ >= 0 (We don't want a negative amount of batches)

create Objective coeffation

obj_coeff <- c(13,23,30)

constraints matrix

constraints <- matrix(
  c(
    5,15,4,
    4,4,10,
    35,20,15,
    5,10,20
  ), nrow =4, byrow= TRUE
)

rename column and row names

colnames(constraints) = c("Strwaberry" , "Orange" , "Grape")
rownames(constraints) = c("CO2" , "Water" , "Flavor" , "Production Time")
View(constraints)

create direction vector

direction_c <- c("<=","<=","<=","<=") 

create resources vectore

resources <- c(480,160,1190,200) # 200 = number of employee * work hours * work day

create linear programming object

solve_lp <- lp(
  "max", # find max result
  obj_coeff,
  constraints,
  direction_c,
  resources
)

solve_lp$objval # Objective value
solve_lp$solution # solution