Solve maximization or minimization problems using the principles of linear programming. Interpret the feasible region of a linear programming and apply the simplex method to solve problems. Make sure to include correct mathematical procedures and provide clear and complete explanations and interpretations. In the case that the result is decimal, you will round it to two decimal places.
3. A stereo equipment manufacturer makes three types of stereo systems, I, II, and III, with profits of $ 20, $ 30, and $ 40, respectively. You cannot do more than 100 type I systems per day. Type I systems require 5 man hours and the corresponding numbers of man hours for types II and III are 10 and 15, respectively. If the manufacturer has 2,000 man-hours per day available, it determines the number of units of each system that must be manufactured to maximize profit. Use the principles of linear programming to find the corresponding gain.
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