A week after the Ministry of Heavy Industries
rescued Glasgow’s shipyards from closure, it announced that the Royal Navy warships will be built in Scotland, provided the labor unions withdraw their protests.
Because all events happened in the past, the use of "will be" is unacceptable. Therefore eliminate A, D and E.
Consider B and C, it's quite a tricky sentence since the past perfect action happens before certain event that is the conclusion of the action.
Timeline: (1) earliest => (2) past => (3) now
Timeline in this sentence: (1) the Ministry rescued => (2) it announced that => (3) provided the labor unions withdraw
Remember rule of past-perfect tense is: if there are two events in the past A and B, past-perfect tense is appropriate use if event A must end when event B interrupts it.
Then,
it had announced ...
the labor unions withdrew their protests.
Hence C correct.
(A) rescued Glasgow’s shipyards from closure, it announced that the Royal Navy warships
will be(B) rescued Glasgow’s shipyards from closure, it
announced that the Royal Navy warships would be
(C) rescued Glasgow’s shipyards from closure, it had announced that the Royal Navy warships would be(D) had rescued Glasgow’s shipyards from closure, it announced that the Royal Navy warships
will be(E) had rescued Glasgow’s shipyards from closure, it had announced that the Royal Navy warships
will beCorrect me if I'm wrong.