Larry has 4-cent stamps and 11-cent stamps, which he can combine to produce various amounts of postage. For example, he can make 48 cents by using four 11-cent stamps and a 4-cent stamp. However, there are some amounts of postage he can't make exactly, such as 10 cents.
What is the largest number of cents that Larry CANNOT make exactly from a combination of 4- and/or 11-cent stamps?
Explain how you know your answer is correct. (You should explain two things: why Larry can't make the amount of your answer, and why he CAN make any bigger amount.)