1.
f=[-3,-1,0,0]; A=[2,-1,0,0]; b=[12]; Aeq=[3,3,1,0 4,-4,0,1]; beq=[30,16]; lb=[0,0,0,0]; ub=[]; [x,y] = linprog(f,A,b,Aeq,beq,lb,ub)
Optimal solution found.
x =
6.999999999999999
3.000000000000000
0
0
y =
-23.999999999999996
library("Rglpk") #a numeric vector representing the objective coefficients. obj <- c(-2,-1,3,-5) #a numeric vector or a (sparse) matrix of constraint coefficients. mat <- matrix(c(1,2,1,2,3,0,4,-1,1,-1,1,1), nrow = 3) #a character vector with the directions of the constraints. dir <- c("<=", "<=", "<=") #a numeric vector representing the right hand side of the constraints. rhs <- c(6,12,4) Rglpk_solve_LP(obj, mat, dir, rhs, max = FALSE)
$optimum
[1] -22.66667
$solution
[1] 0.000000 2.666667 0.000000 4.000000
2.
f=[-2,-1,3,-5]; A=[1,2,4,-1 2,3,-1,1 1,0,1,1]; b=[6,12,4]; Aeq=[]; beq=[]; lb=[0,0,0,0]; ub=[]; [x,y] = linprog(f,A,b,Aeq,beq,lb,ub)
Optimal solution found.
x =
0
2.666666666666667
0
4.000000000000001
y =
-22.666666666666671
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