Two construction companies, Giant and Sky, bid for the right to build in a field. The possible bids are $ 10 Million, $ 20 Million, $ 30 Million, $ 35 Million and $ 40 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Giant is the winner and will get the field. Giant has ordered a survey and, based on the report from the survey, concludes that getting the field for more than $ 35 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). Sky is not aware of this survey.

(a) State reasons why/how this game can be described as a two-players-zero-sum game [5 Marks]

(b) Considering all possible combinations of bids, formulate the payoff matrix for the game. [5 Marks]

(c) Explain what is a saddle point. Verify: does the game have a saddle point? [5 Marks]

(d) Construct a linear programming model for Company Giant in this game. [5 Marks]

(e) Produce an appropriate code to solve the linear programming model in part (d). [5 Marks]

(f) Solve the game for Giant using the linear programming model and the code you con- structed in parts (d) and (e). Interpret your solution. [5 Marks]