Given the equation of X, y | 6-x | + | X-2 | + | y + 2 | + | y + 3 | = 5, try to find the maximum and minimum value of XY It's still that sentence

Given the equation of X, y | 6-x | + | X-2 | + | y + 2 | + | y + 3 | = 5, try to find the maximum and minimum value of XY It's still that sentence

(1) when x > 6
If y ＞ - 2, then
The left side of the original formula = X-6 + X-2 + y + 2 + y + 3 = 2x + 2y-3 ＞ 2 × 6 + 2 × (- 2) - 3 = 5
If - 3 ≤ y ≤ - 2, then
The left side of the original formula is X-6 + x-2-y-2 + y + 3 = 2x-7 ＞ 2 × 6-7 = 5
If y ＜ - 3, then
The left side of the original formula = X-6 + x-2-y-2-y-3 = 2x-2y-13 ＞ 2 × 6-2 × (- 3) - 13 = 5
(2) when 2 ≤ x ≤ 6
If y ＞ - 2, then
The left side of the original formula is 6-x + X-2 + y + 2 + y + 3 = 2Y + 9 ＞ 2 × (- 2) + 9 = 5
If - 3 ≤ y ≤ - 2, then
The left side of the original formula is 6-x + x-2-y-2 + y + 3 = 5
If y ＜ - 3, then
The left side of the original formula = 6-x + x-2-y-2-y-3 = - 2y-1 ＞ - 2 × (- 3) - 1 = 5
(3) when x ＜ 2
If y ＞ - 2, then
The left side of the original formula is 6-x + 2-x + y + 2 + y + 3 = - 2x + 2Y + 13 ＞ - 2 × 2 + 2 × (- 2) + 13 = 5
If - 3 ≤ y ≤ - 2, then
The left side of the original formula is 6-x + 2-x-y-2 + y + 3 = - 2x + 9 ＞ - 2 × 2 + 9 = 5
If y ＜ - 3, then
The left side of the original formula is 6-x + 2-x-y-2-y-3 = - 2x-2y + 3 ＞ - 2 × 2-2 × (- 3) + 3 = 5
It can be seen that the left side of the original formula is larger than the right side except when 2 ≤ x ≤ 6 and - 3 ≤ y ≤ - 2
therefore
When x = 2 and y = - 2, the maximum value of XY is - 4
When x = 6 and y = - 3, the minimum value of XY is - 18