3. Two mining companies, Red and Blue, bid for the right to drill a eld. The possible bids are $3 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), Red is the winner and will get the eld. Company Red has ordered a geological survey and, based on the report from the survey, concludes that getting the eld 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-zerosurn 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 Red 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 Red using the linear programming model and the code you con- structed in parts {(1) and (e). Interpret your solution. [5 Marks] 4. Consider two companies, Company A and Company B, producing the same model of iPhones. The demand for the iPhones produced by Company A is D A, and the demand for the iPhones produced by Company B is D3. The demands are described by the following functions: DA=200PA(PAP) (l) D3=QUUPB(PBP) (2) where PA and P3 are the prices of iPhones for Factory A and Factory B respectively, and P is the average price over the prices PA and PB. For each company, the cost for producing one iPhone is C = 20. Suppose that each company can only choose one of the three prices {61], 70,80} for a sale. (a) Compute the prots of each company under all sale price combinations and produce the payoff matrix for each company. int: t epro t = t e eman or t ei ones X t e pro t o onei one er e. h h (1 cl f h Ph h E f Ph aft sal [10 Marks] (b) Find the Nash equilibrium of this game. What are the prots at this equilibrium? Explain your reason clearly. [5 Marks] (C) If the cost 0 doubles to C = 40, would the Nash equilibrium from part (b) change? Give clear reasons. [5 Marks]