India Tea Company holds two kinds of tea leaves in its inventory - Grade 1 and Grade 2. The quantity of Grade1 tea held in inventory is currently 750 kg and the quantity of Grade2 tea held in inventory is currently 1200 kg. The two types of tea are then mixed in two types of packages weighing one kilogram each - the Economy pack and the Special pack. The economy pack consists of grade1 and grade2 types of tea in a ratio of 1:3, while the special pack combines the two categories of tea in equal proportion. The profit margins on the Economy pack and the Special pack are Rs5/- and Rs8/- respectively.

1. Formulate the above as a linear programming problem.
2. Draw a neat diagram and identify the optimal point.
3. Would your answer be different if the profit margin on a special pack is Rs 10/- per pack? Show your working and then come to your conclusion.
4. If the profit margin of a special pack is Rs. 10/pack, would the optimal point be unique? Why?