1. A food factory is making a beverage for a customer from mixing two different existing products A and B. The compositions of A and B and prices ($/L) are given

as follows, A B Amount (L) in /100 L of A and B Lime Orange 6 2 7 4 Mango 4 8 Cost (S/L) 4 12 The customer requires that there must be at least 5 Litres (L) Orange and at least 5 Litres of Mango concentrate per 100 Litres of the beverage respectively, but no more than 6 Litres of Lime concentrate per 100 Litres of beverage. The customer needs at least 140 Litres of the beverage per week. a) Explain why a linear programming model would be suitable for this case study. [5 marks] b) Formulate a Linear Programming (LP) model for the factory that minimises the total cost of producing the beverage while satisfying all constraints. [5 marks] c) Use the graphical method to find the optimal solution. Show the feasible region and the optimal solution on the graph. Annotate all lines on your graph. [5 marks] Note: you can use graphical solvers available online but make sure that your graph is clear, all variables involved are clearly represented and annotated, and each line is clearly marked and related to the corresponding equation. d) What is the range for the cost ($) of A that can be changed without affecting the optimum solution obtained above? [5 marks]