SIT718 Real World Analytics Assignment

QUESTION 1

a) Explain why a linear programming model would be suitable for this case study.

b) Formulate a Linear Programming (LP) model for the factory that minimises the total cost of producing the beverage while satisfying all constraints.

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. What is the minimal cost for the product?

d) Is there a range for the cost ($) of A that can be changed without affecting the optimum solution obtained above?

Question 2 -

a) Formulate an LP model for the factory that maximises the profit, while satisfying the demand and the cotton and wool proportion constraints.

b) Solve the model using R/R Studio. Find the optimal profit and optimal values of the decision variables.

Question 3 -

(a) Give reasons why/how this game can be described as a two-players-zero-sum game.

(b) Formulate the payoff matrix for the game.

(c) Explain what is a saddle point. Verify: does the game have a saddle point?

(d) Construct a linear programming model for each player in this game;

(e) Produce an appropriate code to solve the linear programming model in part (c).

(f) Solve the game for David using the linear programming model you constructed in part (c). Interpret your solution.