(Solved): 1. You have solved a 3-variable maximisation Linear Program with the objective function of z = 4x ...

1. You have solved a 3-variable maximisation Linear Program with the objective function of z = 4x? + 3x? + 7x3. The Linear Program has two "<" constraints, and its optimal solution is as follows: (X?, X?, X3, S?, S?) = (7, 0, 0, 2, 0), z* = 28. Consider the following situations: • The objective function changes to maximise z = 4x? + 7x? + 7x3. • The objective function changes to maximise z = 3x? + 3x? + 7x3. For each situation above, analyse separately and specifically what must be checked if you were to determine whether the current basis remains optimal after the change is made. Justify your answers. (CO3, C4) [4 marks]