Let y = # coats made
Total wool cannot exceed 200 sq. yds, so
Total labor cannot exceed 300 hrs, so
Since you cannot make a negative number of slacks and coats,
Graph each inequality and find the feasible region. Locate the vertices of the feasible region by finding the intersection of the respective linear equations that bound it. Use the profit function P to determine the profit at each vertex. When P is maximized, you have found your optimum production run.
This would be a whole lot easier if you could use a graphing calculator. Can you?