For the first three questions, there was a penalty of -1 for not including the problem statement and another (-1) for not giving a solution summary. The problems are out of 10 each. No points were removed for not including problem statement/solution summary for the last 2 problems. Q.1) This problem was well done overall, except for the fact that several people forgot the fact that the percentages for each mix must add up to 1, when summed over all the juices. Q.2) The formulation and solving was quite well done in general. However, many people did not do well in the last parts of this question Q.3) This problem was well done overall. Q.4) This problem was also well done overall, except that several people computes a basis for the column vectors of the matrix, rather than for the row vectors as required by the question. Q.5) This problem was very well done in general.