Show the feasible region and the optimal solution the graph
SIT718 Real world Analytics Assessment Task 3
Total Marks = 100, Weighting - 30%Your final submission should consist of:
1. “name-report.pdf”: A pdf file (created in any word processor) with up to 8 pages, con- taining the solutions of the questions, labelled with your name;
2. “name-code.R”: Two codes combined in one with your R file, labelled with yourname.R, with lp models for Questions 2 and Questions 3.
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 ($/L) are given as follows,
| Amount (L) in /100 L of A and B | |||||
|---|---|---|---|---|---|
|
Cost ($/L) | ||||
| A B |
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.
d) Is there a range for the cost ($) of A that can be changed without affecting the opti-mum solution obtained above?
[5 marks]
| Purchase price | |
|---|---|
|
The maximal demand (in tons) for each product, the minimum cotton and wool propor-tion in each product is as follows:
[10 Marks]
b) Solve the model using R/R Studio. Find the optimal profit and optimal values of the decision variables.
| Winning Chip | |
|---|---|
| Red beats white White beats blue Blue beats red Matching colors |
|
(a) Formulate the payoff matrix for the game and identify possible saddle points.
[Hint: Each player has the same strategy set. A strategy must specify the first chip chosen, the second and third chips chosen. Denote the white, red and blue chips by W, R and B respectively. For example, a strategy “WRB” indicates first choosing the white and then choosing the red, before choosing blue at the end.]
4. Three board members are going to vote for a president from them: Ava, Bob and Chloe. Each member is both a candidate and a voter. Here is the voting rule: each member votes for one candidate (voting for oneself is allowed); if two or more people vote for the same candidate then that person is chosen as the president; if there is exactly one vote for each candidate, then the person for whom Ava voted is selected as the president.
[6 Marks]
(c) Find the Nash equilibrium of this game. Explain your reason clearly.
[6 Marks]
