Brain Thumper #8 The Pacific Proprietary Production Plant has the capacity to manufacture straight sections of miniature railroad track on two machines, each of which produces a specific length of track. For instance, suppose that the company had initially configured the machines to make straight track that is 3 cm and 5 cm long. A hobbyist who buys this track would be able to use different combinations thereof. For instance, she could combine one 3 cm section and one 5 cm section to fill an 8 cm gap in her modeling project. Three 3 cm sections make 9 cm, two 5 cm sections make 10 cm, and so forth. However, there are some shorter integer lengths that cannot be achieved. In this case it is impossible to get straight track in 1, 2, 4, or 7 cm segments. As it turns out, given the way that the two machines were configured, there are exactly eight different positive integer lengths that cannot be constructed. Find at least one possibility for the plant's machine specifications. Note, however, that requirements in the way tracks couple prohibit the manufacture of a section that is 2 cm or shorter.