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3. Two mining companies, Fox and Trot, bid for the right to drill a field. The possible bids are $ 15 Million, $ 25 Million, $ 35 Million, $ 45 Million and $ 50 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Fox is the winner and will get the field. Fox has ordered a geological survey and, based on the report from the survey, concludes that getting the field for more than $ 45 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). (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 Trot in this game. (5 Marks) (e) Produce an appropriate code to solve the linear programming model in part (d). [5 Marks] (1) Solve the game for Trot using the linear programming model and the code you con- structed in parts (d) and (e). Interpret your solution. [5 Marks]