The machine is to be redesigned.

根据试题的选项设置，应该是按照“be动词后可接不定式分句”(例如Collins Cobuild English Usage的be词条7有类似的解释)来设计的。这个句子也可以换种方式解释: 把be to解释为情态习语，后接省略to的不定式，因为the machine与redesign在逻辑语意上构成被动关系，故而使用不定式的被动形式。试对比：

1) The machine should/must be redesigned.

2) The machine is going to be redesigned.

此外，关于be to的处理，查阅并阅读了一下外版材料，语法学者们的处理不尽相同。L.G.Alexander按照The use of 'am/is/are to处理；Collins Cobuild English Usage在be词条处理为“You sometimes use to-infinitives clauses after be"; Bas Aarts把be to处理为modal idiom，同时还采用了Rodney Huddleston的解释；Rodney Huddleston按照quasi-modal be解释；章振邦教授把be to解释为semi-auxiliary。当然，be to的术语名称和其用法相比，并不是那么重要。如果感兴趣的话，可以阅读以下材料：

1. L.G.Alexander的Longman English Grammar 9.48.1 The use of 'am/is/are'部分

2. Bas Aarts的Oxford Modern English Grammar 10.3.10 Modal idioms和10.3.10.3 BE[to]部分

3. Rodney Huddleston的The Cambridge Grammar of the English Language Quasi-modal be部分

4. Randolph Quirk的A Comprehensive Grammar of the English Language 3.45 Modal Idioms: had better,etc，3.46 The meanings of the modal idioms(d)和4.47Concluding comments on constructions expressing future time部分

5. 章振邦《新编高级英语语法》6.1C半助动词部分

至于Huddleston所说的quasi-modal，Bas Aarts是这样解释的: The label 'quasi-modal' indicates that in spite of its one modal property(and its modal meaning) this be doesn't in fact qualify grammatically for inclusion in that class.