Question

x and y are two non negative numbers such that 2x+y=10 the sum of maximum and minimum values of x+y ​

Answer 1

First of all, determine the function as 'f'. Then transform the function into one variable using the equation given in the question. In this question, it is given that,

x+y=60.

So y=60-x.

As I said earlier we have to write f=x*y.

Now we can write f as a function of 'x'.

f=x(60-x).

f(x)=60*x-x^2.

Now differentiate f(x) with respect to x and equate to '0' as shown below.

f '(x)=60-2*x=0

Implies, x=30. If x=30, then according to equation y should be 30.

So the maximum value of xy is 900.

OR

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