Question 1 As part of the nation's vaccination programme for children, all citizens below the age of six need to be vaccinated with a cocktail mixture of Vaccine W, Vaccine X and Vaccine Y. One litre of the cocktail mixture requires a certain minimum amount of active compound alpha, beta, gamma and theta as shown in Table 1. Active Alpha Beta Gamma Theta Compound Quantity in 45 20 40 5 Millilitre Table I Table 2 shows the composition of Vaccine W, X and Y as well as cost of the vaccines. A pharmaceutical factory is considering the least cost way to produce one litre of the cocktail mixture. Active compound in millilitre per litre of vaccine Vaccine Alpha Beta Gamma Thera Cost per Litre W 60 40 20 0 60 X 40 15 40 5 50 Y 30 40 60 10 120 Table 2 (a) Develop a complete Linear Programming (LP) model that represents the problem above to achieve an economically optimal solution. You are not required to solve it at this stage. (10 marks) (b) The chief scientist has issued a new guideline, stating that the cocktail mixture of vaccine is deemed completed as along as at least three of the active compounds are fulfilled. Implement this new guideline in your LP model in Question I(a) to include the new information. (Hint: Please search online on "linear programming with conditional constraint" or "linear programming with binary". (10 marks) (c) Use the Excel Solver to solve the optimal solution to the problem in Question I(b) and summarise how the cocktail mixture should be formulated using the available Vaccine W, X, and Y. Please paste here three screenshots, (1) the problem worksheet just before clicking the Solver command, (2) the Solver Parameters dialog just before clicking Solve and (3) the Answer Report created by the Solver. Please limit the answer to within three pages. (20 marks)