A medicinal chemist working in a Singapore-based pharmaceutical company has been tasked to develop a nutritional supplement which should contain a total of at least 16 units of Magnesium and 24 units of Zinc by mixing two commercially available food grade compounds: C1 and C2.

C1 costs $140 per kg while C2 costs $180 per kg. According to the supplier, every kg of C1 contains 4 units of Magnesium and 2 units of Zinc, while every kg of C2 contains 2 units of Magnesium and 4 units of Zinc.

How should the chemist minimise the cost of such a mixture?

1. Find the optimal solution to the problem using the graphical method or any other manual method (show your workings) and explain by using the graph whether the optimal solution is unique.
2. Due to other nutritional considerations, the chief chemist has given the medicinal chemist additional instruction that the quantity of compound C2 should be at most (alpha) times the quantity of compound C1 used (alpha> 0). Using the graphical method, explain how the optimal solution in this new situation could be affected by differing values of (alpha> 0). You are required to re-work the new optimal solution, if different from (b). Please limit your answer to within two pages.