Linear Programming with LINDO

A) Solve the discrete-valued LP using LINDO-MIP. Add the necessary constraints to allow solution by the LINDO-MIP solver. ONLY one MIP must be solved to provide the solution. Write out the LINDO-MIP program first (and include any comment statements which explain your model). Recall from the class notes that you should introduce and use additional integer (0,1) variables to setup the program in LINDOMIP format. An additional consideration is that you must use the smallest number of integer (0,1) variables. [Hint: Use Binary Expansion for variable X3 and show all work.]

B) Solve the discrete-valued LP again, using LINDO-MIP. Add the necessary constraints to allow solution by the LINDO-MIP solver. ONLY one MIP must be solved to provide the solution. Write out the LINDO-MIP program first (and include any comment statements which explain your model). Recall from the class notes that you should introduce and use additional integer (0,1) variables to setup the program in LINDO-MIP format. But in this case should use (add) GIN variable(s) where appropriate. However you must still add the smallest number of additional integer (0,1) variables where necessary.

s.t. Consider the following discrete-valued problem: Minimize z 4 xl + 2 x2 + 5 x3 X2 + X3 36 (1) X3 16 (2) 4x1 + 4x3 42 (3) X1 (1,2,3,4,6.3,8); X2 (0,2,4,6,7.5,8,11); X3 (0,1,2,3,4,5,6,7,8,9,10,11,12) Xl + x1 X2 +