A large commercial ship company has two types of engineers working on its ships:

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A large commercial ship company has two types of engineers working on its ships: engineers (E) and chief engineers (C). For simplicity, we assume that attrition occurs only once a year (on the 31st of December) and all hiring occur once a year (on the 1st of January). Each year, it is estimated that the company hires 12 chief engineers and 48 engineers. Further, each year. 50% of its chief engineers will retire (maybe forcibly). 50% of its engineers will remain engineers, while the rest of the engineers will either be promoted to chief engineer (call this fraction c) or be tired. Assume that the company currently (at the end of the day 011 .January 1st of year 0) has 12 chief engineers and 48 engineers. Denote by [et ; et] the column vector representing the number of chief engineers and engineers with the company on the first of January of year t. Define a matrix A and a vector b that allow you to relate [et + 1;et + 1] and[ct ; et]. Use 1. find an expression for [et ; et] as a function of .A and b. What should the value of c be. so that, when t is large, the number of chief engineers equals the number engineers. In answering this question, you might find useful to remember that

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