Mathematics Homework Help

Q1) 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?

(1a) Develop an LP model that represents the problem by clearly stating the decision
variables, objective and constraints. You are not required to solve it at this stage.
Please limit your answer to within one page.
(15 marks)

(1b) 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.
(20 marks)

(1c) Due to other nutritional consideration, the chief chemist has given the medicinal
chemist an additional instruction that the quantity of compound C2 should be at most
 times the quantity of compound C1 used ( > 0). Using the graphical method,
explain how the optimal solution in this new situation could be affected by differing
values of  ( > 0). You are required to re-work the new optimal solution, if different
from (b). Please limit your answer to within two pages.
(20 marks)

Q2) Describe one application of Linear Programming in healthcare, hospitality, manufacturing, or
supply chain. You are required to describe the scenario and explain how LP could be used in
solving the scenario. You do not need to formulate the problem into an LP model or solve it.
Please limit the answer to within 500 words.
(45 marks)