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 Sky 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 Sky using the linear programming model and the code you constructed in parts $($d$)$ and $($e$).$ Interpret your solution.

$[$