Let X and y satisfy the constraint conditions {- x + Y-2 ≤ 0, x + y-4 ≤ 0, x-2y + 2 ≤ 0} if the sum of the maximum and minimum of the objective function z = ax + y (a > 0) is 5 / 2, then the value of real number a is

Let X and y satisfy the constraint conditions {- x + Y-2 ≤ 0, x + y-4 ≤ 0, x-2y + 2 ≤ 0} if the sum of the maximum and minimum of the objective function z = ax + y (a > 0) is 5 / 2, then the value of real number a is

Y = - ax + Z, because a ＞ 0, the line passes through the intersection of one or three lines, which is the minimum value at this time. Substitute the point (- 2,0) z = - 2A, and continue to move upward. Two critical points (1,3), (2,2) are obtained. They are brought into the test, leaving (1,3) that is - 2A + A + 3 = 5 / 2, so a = 1 / 2

If the function f (x, y) is continuous on the bounded closed domain D, then f (x, y) must obtain the maximum and minimum values on D

Wrong
For example, the tangent function between - 90 degrees and + 90 degrees is continuous, but has neither maximum nor minimum

Find the function z = x ^ 2 + y ^ 2-12x + 16y in the bounded closed interval region x ^ 2 + y ^ 2

z=x^2+y^2-12x+16y=(x-6)²+(y+8)²-100
(X-6) &# - 178; + (y + 8) &# - 178; denotes the square of the distance from the moving point (x, y) to the fixed point (6, - 8),
Bounded closed interval domain x ^ 2 + y ^ 2