We can easily see that x1 = x2 = x3 = 1 is a feasible point for the following linear program: Maximize w = 4x1 + 2x2 + 3x3 Subject to: 2x1 + 3x2 + x3 S 12 X1 + 4x2 + 2x3 5 10 3x1 + x2 + x3 = 10 X2, X2, X, 20 a) Write this LP with slack variables. What are the values of the slack variables? What is the value of the objective function? b) Without solving the problem, identify variables are basic and which are non-basic. c) What is the dual of this LP? Write it in minimum form with all surplus variables. d) List all the pairs of complimentary variables in your primal and dual LP. e) Find any feasible point for the dual. What are the values of all the dual variables (including slack variables)? What is the value of the dual objective function at this point? f) Multiply together the values of all the pairs of complimentary variables (giving 6 products) then add them together. What do you get? Compare this to the difference between the value of the dual objective function you calculated in (e) and the value of the primal objective function from (a). What do you notice? g) Solve both the primal and the dual LPs (you can use a solver). What are the values of all the variables? What do you notice about each of the pairs of complimentary variables? This is a property of primal/dual linear programs called Tucker Duality