Question

two non-negative real number x and y are such that 2x + Y equal to 5 the sum of maximum and minimum value of x + Y is​

Answer 1

Given :  two non-negative real number x and y are such that 2x + Y = 5

To find :  sum of maximum and minimum value of x + Y

Solution:

2x  + y  = 5  ,    x ≥ 0  , y ≥ 0

=> x + x + y   = 5

=> x + y  = 5  - x

=> x + y would be maximum when   x  is minimum (x  = 0)

=> x + y maximum value = 5 - 0 = 5

max value of x + y   =  5

minimum value of  x + y  would be when x  is maximum

lets find max value of

2x + y = 5

=> 2x  = 5 - y

2x  or x would be maximum when  y = 0

=> 2x =5  => x  = 5/2

putting  x  = 5/2  

minimum value of x + y = 5 - 5/2

=> minimum Value of x + y = 5/2

max value of x + y   =  5

minimum Value of x + y = 5/2

Sum of maximum and minimum value of x + Y = 5  + 5/2   =  15/2

15/2  is the sum of maximum and minimum value of x + Y

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