questions 1, 2,3,4

1.
1)
Standard form the linear programming problem by introducing slack variables S1,S2,S3,S4
Max Z = 2x1+8x2-x3-2x4+0S1+0S2+0S3+0S4
s.t 2x1+3x2+6x4+0S3=6
-2x1+4x2+3x3+0S4=1.5
3x1+2x2-4x4+0S3=6
    x1, x2, x3, x4, S1,S2,S3,S4≥0
2)
Duality of minimization
Max Z = 2x1+8x2-x3-2x4
s.t 2x1+3x2+6x4≤6
-2x1+4x2+3x3≤1.5
3x1+2x2-4x4≤6
    x1, x2, x3, x4≥0
3)
4)
R-code
# Import lpSolve package
library(lpSolve)
# Set coefficients of the objective function
f.obj <- c(2, 8, -1, -2)

# Set matrix corresponding to coefficients of constraints by rows
# Do not consider the non-negative constraint;...