Three non negative numbers a, B, C, satisfy 2A + B-C = 5, A-B + 2C = 7, find the minimum value of a + B + C

Three non negative numbers a, B, C, satisfy 2A + B-C = 5, A-B + 2C = 7, find the minimum value of a + B + C

c=12-3a
b=17-5a
a+b+c=29-7a
The larger a is, the smaller the value is
Because b > = 0
A maximum of 3
The minimum value is 7
a=3、b=2、c=3

The non negative numbers a, B, C satisfy a + B + C = 30, 3A + B-C = 50, and find the maximum and minimum of n = 5A + 4B + 2C

3a+3b+3c=90,3a+b-c=50
So n = 140-a
From the solution of a + B + C = 30, 3A + B-C = 50
b=40-2a
c=a-10
Because a, B, C are nonnegative
So 40-2a ≥ 0, a ≤ 20,
a-10≥0,a≥10
So 120 ≤ n ≤ 130
The maximum and minimum values are 130 and 120, respectively

If nonnegative numbers a, B and C satisfy a + B-C = 2 and A-B + 2C = 1, then the sum of maximum and minimum of S = a + B + C is ()
A. 5B. 9C. 10D. 12

A + B = C + 2, A-B = 1-2c, a = 12 (3 − C) B = 12 (1 + 3C), ∵ a, B are non negative numbers, ∵ 12 (3-C) ≥ 0, 12 (1 + 3C) ≥ 0, the solution is - 13 ≤ C ≤ 3, ∵ C is also non negative, ∵ 0 ≤ C ≤ 3, ∵ s = a + B + C = 12 (3-C) + 12 (1 + 3C) + C = 2C + 2, ∵ when C = 3, s is the largest