(of corve thе ппен program (yor по потпеец то цветне затрех вечнозу: (e) Write down the dual of your linear program from part (a). (d) Solve the dual program (you do not need to use the simplex method). 4.2 (due Nov. 9) Give a mathematical expression (sums are allowed: linear programs are NOT allowed) for the value of the two person zero-sum game with the following n x n payoff matrix 1 0 0 02 P- 0 0 0 " (More precisely, the matrix P is defined by Pi and P-0 for ij). (Hint: Solve for small n first and then generalize. For example, for n = 2 solve the following linear program: min : (69)(2)(:) +1 20.20; we are using the convention that the entries in the matrix are the payoff for the row player.) 4.3 (due Nov. 9) Zofka is trying to measure the length of a race track using a car. The (digital) odometer in the car shows the number of kilometers traveled since the car was made. She drives around the track and each time she crosses the finish line she writes down the number on the odometer. She wants to infer the length of the race track from these numbers in the following sense: 1) she wants to know the minimal possible track length that is consistent with the measurements and 2) she wants to know the maximal possible track length that is consistent with the measurements. Example input: suppose Zofka took one lap around the track. When she crossed the finish line at the beginning of the first lap the odometer showed 713. When she crossed the finish line at the end of the first lap the odometer