Cho bài toán quy hoạch tuyến tính sau:  
 
 

1 2 3 4 5
1 2 3
2 3 4
2 5
1 ( ) 2 6 4 2 3 min
2 4 60
2 4 2 68
3 44
3 0; 1,5 j
g x x x x x x
x x x
x x x
x x
x j
     
    
   

  
 
a) Tìm bài toán đối ngẫu của bài toán trên.
b) Giải bài toán gốc bằng phƣơng pháp đơn hình rồi suy ra kết quả của bài toán đối
ngẫu.

What is the first quartile of this data set? 10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38 a. 12 b. 19 c. 29 d. 10

What is the ratio of the length of an object in yards to the length of the same object in miles?

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.