5 problems, 15 pts each. Name____________________________

On the scantron, choose one of 5 answers. Use #2 pencil.

For me, write down details.

6-8. Matrix game is given by its payoff matrix.

6.

0 |
2 |
3 |
4 |
5 |
3 |
3 |

0 |
1 |
4 |
5 |
4 |
6 |
3 |

1 |
2 |
6 |
5 |
5 |
7 |
0 |

0 |
0 |
1 |
1 |
4 |
2 |
0 |

1 |
1 |
4 |
3 |
2 |
4 |
0 |

3 |
2 |
2 |
3 |
3 |
6 |
3 |

7.

1 |
2 |
3 |
1 |
2 |
4 |
3 |

3 |
1 |
4 |
4 |
2 |
4 |
0 |

3 |
3 |
2 |
0 |
4 |
3 |
1 |

4 |
1 |
4 |
0 |
2 |
3 |
2 |

3 |
1 |
2 |
4 |
2 |
1 |
3 |

(A) [0,0,0.5,0,0.5], (B) [1/2, 1/2, 0, 0, 0], (C) [0,0, 0,0.5,0.5], (D) [1/2, 0, 0, 0, 1/2], (E) [1/2, 1/2, 0].

8.

2 |
0 |
2 |
2 |

2 |
1 |
1 |
2 |

4 |
2 |
0 |
1 |

9. Consider the system of two equations for two unknowns x, y, where t is a given number:

x+ty = 3, 2x+t

(A) the system is not linear because the second equation is not linear,

(B) there is t such that the system has no solutions,

(C) there is t such that the system has infinitely many solutions.

(D) the system cannot be solved, (E) 0 = 1.

10. An optimal solution x for

2x

is (A) 0 , (B) 1, (C) 2, (D) 3, (E) 2.5.