Larry C. answered • 04/15/20
Computer Science and Mathematics professional
Since the base equation is minimized when the x.y pair has the largest possible y paired with the smallest possible x, we can look at the 3rd inequality to see that the largest possible value of y is 4.
Plugging 4 into the 2nd inequality gives 8 - 5x ≥ -4 -> 12 ≥ 5x -> 2.4 ≥ x which gives an upper limit for x but not a lower.
Plugging 4 into the 1st inequality gives 3x+16 ≥ -8 -> 3x ≥ -24 -> x ≥ -8 which give a lower limit for x, thus
-8 ≥ x ≥ 2.4
So the minimum value of f(x,y) is at (-8,4) with a value of 3(-8) - 2(4) -> -24-8 -> -32
The maximum value will be the largest value of x paired with the smallest value of y. We already determined the maximum value of x is 2.4
2y - 5(2.4) ≥ -4 -> 2y -12 ≥ -4 2y ≥ 8 -> y ≥ 4
Since y ≥ 4 but also y ≤ 4, y must equal 4.
So the maximum value of f(x,y) is at (2.4,4) with a value of 3(2.4) - 2(4) -> 7.2 - 8 -> -0.8
