Suppose an airline is flying a 10-seat plane from washington d. c. to chicago. suppose tickets on the flight cost $300 and passengers who buy tickets fail to show up for their flight 10% of the time. if a passenger doesn’t show up, they forfeit the cost of the ticket. the airline can overbook the flight, i. e., it can sell more than 10 tickets even though the plane only has 10 seats. however, if a passenger with a valid ticket arrives for the flight and cannot be seated, the airline will have to refund her $300 and pay compensation of $100. if the airline wants to maximize profits, how many tickets should it sell?

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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