Basic feasible solution, permuting the row

[pinki82]

FOr the problem,
Max(-x_1 - 2x_2 + 3x_5)
x_1 + x_2 + 2x_3 + 3x_4 + x_5 <= 1
2x_1 - x_2 + 4x_3 + 6x_1 - x_5 <= 2
x_j >= 0, j= 1,...,5

A) show that x_1 = 1, x_2= x_3= x_4= x_5 = 0 is a basic feasible solution.
B) Find two different dictionaries..(i.e. Not obtained by permuting the rows) that have this point as a basic solution.
C) How many different dictionaries have this point as basic solution.

i am so lost.. especially in part b and c.
please help..any hint or help would be really appreciated!
thanks.

 

[Aaron Bex]

A) To show that x_1 = 1, x_2= x_3= x_4= x_5 = 0 is a basic feasible solution, we must first make sure that it satisfies all of the constraints. The given solution satisfies all of the constraints, as it meets each constraint's lower bound (zero), and does not exceed the upper bound. Therefore, this solution is a basic feasible solution.

B) Two different dictionaries that have this point as a basic solution are:

Dictionary 1:
x_1 = 1 (basic)
x_2 = 0 (non-basic)
x_3 = 0 (non-basic)
x_4 = 0 (non-basic)
x_5 = 0 (non-basic)

Dictionary 2:
x_1 = 0 (non-basic)
x_2 = 1 (basic)
x_3 = 0 (non-basic)
x_4 = 0 (non-basic)
x_5 = 0 (non-basic)

C) The number of different dictionaries that have this point as a basic solution is five, since there are five variables, each of which can be either basic or non-basic.