It is known that x ≥ 0, y ≥ 0, 3x + 4Y = 12; the maximum and minimum of ∣ 2x-3y ∣ are obtained

It is known that x ≥ 0, y ≥ 0, 3x + 4Y = 12; the maximum and minimum of ∣ 2x-3y ∣ are obtained

∵3x+4y=12,x≥0,y≥0
∴x∈[0,4],y∈[0,3]
And ∵ 3x + 4Y = 12, ∣ 2x-3y ∣
∴∣2x-3y∣=∣(17/4)x-9∣
∴∣2x-3y∣∈[0,9]
The maximum value of ∣ 2x-3y ∣ is 9
The minimum value of ∣ 2x-3y ∣ is 0