two non-negative real numbers x and y are such that 2x + Y is equals to 5. the sum of the maximum and minimum values of X + Y is
Answers
Answer:
7.5
Step-by-step explanation:
Two non-negative real numbers x and y are such that 2x + Y is equals to 5. the sum of the maximum and minimum values of X + Y is
2X + Y = 5
X ≥ 0 & Y ≤ 5
Y ≥ 0 & X ≤ 5/2
2X + Y = 5
=> X + X + Y = 5
=> X + Y = 5 - X
X is non negative real number
X should be minimum for Maximum Value of X + Y
X Min = 0
=> (X + Y) Max = 5
X should be maximum for Minimum Value of X + Y
X Max = 2.5
=> X + Y = 5 - 2.5
=> (X + Y) Min = 2.5
(X + Y) Max + (X + Y) Min = 5 + 2.5 = 7.5
Answer: 7.5
Step-by-step explanation:
Two non-negative real numbers x and y are such that 2x + Y is equals to 5. the sum of the maximum and minimum values of X + Y is
2X + Y = 5
X ≥ 0 & Y ≤ 5
Y ≥ 0 & X ≤ 5/2
2X + Y = 5
=> X + X + Y = 5
=> X + Y = 5 - X
X is non negative real number
X should be minimum for Maximum Value of X + Y
X Min = 0
=> (X + Y) Max = 5
X should be maximum for Minimum Value of X + Y
X Max = 2.5
=> X + Y = 5 - 2.5
=> (X + Y) Min = 2.5
(X + Y) Max + (X + Y) Min = 5 + 2.5 = 7.5