已知1≤x y≤3,2≤2x-y≤4,则z=x 3y的最小值= ;最大值=

答案为3和22/3要详细的过程
2025-05-19 20:10:45
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回答(1):

你好!

设 a = x+y,b = 2x - y
解得 x = (a+b)/3,y = (2a-b)/3
z = x + 3y = (a+b)/3 + 2a - b = 7/3 a - 2/3 b
1 ≤ a ≤ 3 ,7/3 ≤ 7/3 a ≤ 7
2 ≤ b ≤ 4,- 8/3 ≤ - 2/3 b ≤ - 4/3
两式相加, - 1/3 ≤ 7/3 a - 2/3 b ≤ 17/3

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