This is a simple equation query

Given all the equations shown in the BLUE box below.

How is the equation underlined in RED determined.

Please show in more detail.

Please explain clearly showing each step as thoroughly as possible. If you are using hand written notes, then please ensure they are neat and legible, as it is difficult to interpret illegible hand-written notes. Alternatively, use LaTex.

X1 2 0, X1 2 0, AT1 = 0, (6.3) 12 2 0, T2 2 0, 121'2 = 0, (6.4) A3 2 0, A3 (1 - x] - ,) = 0, (6.5) P1 + 1 -21341 = 0, (6.6) P2 + 12 - 21312 = 0. (6.7) . The complementary slackness conditions for the first constraint imply that either A1 = 0 or x1 = 0. However, substituting x1 = 0 into (6.6) yields P1 + 1 = 0. Since p1 > 0 and A1 2 0, this is not possible. Substituting M1 = 0 into (6.6) yields: P1 - 213.1 = 0 C1 = P1 213' so that 13 # 0. We therefore have A1 = 0, while: P1 13 > 0. "213' Applying symmetry arguments to the complementary slackness conditions for the second constraint we immediately have 12 = 0 while: P2 13 > 0. 213 Dividing the middle terms of both sets of solutions, we find that: T2 P2