GATE CSE
First time here? Checkout the FAQ!
x
+4 votes
205 views

Solve min $x^{2}+y^{2}$

subject to

       $x + y \geq 10,$

   $2x + 3y \geq 20,$

           $x \geq 4,$

           $y \geq 4.$

  1. $32$
  2. $50$
  3. $52$
  4. $100$
  5. None of the above
asked in Calculus by Veteran (29.5k points)   | 205 views

4 Answers

+4 votes
Best answer
Answer -> Option B) 50

 x>=4 and y>=4 , So we can take both x =5 & y = 5

x+y >= 10 => Satisfied , 5+5 = 10

2x + 3y >= 20. Satisfied.

This is infact minimum value.

Other options =>

4,4 => x+y constraint fail

4,5 => x+y fail

6,4 => Still giving 52 as sum which is more than 50 !,  This can not  be answer.

7,3 => 49+9 > 58 > 50.
answered by Veteran (41.4k points)  
selected by
+1 vote
I think it's the easiest one,
approach - first we just break to the minimum conditions so every thing can be meet. minimum value such that every thing can satisfy is 5 , 5 which gives = 50,

now all the possiblities are decreasing one number and increasing one. but as u think . as u will decrease one number the value that will decrease will be less then the after effect of increasing the other number.
like 4 and 6 . value that decreases due to decreasing it from 5 is (25-16) = 9

but the increase in the value due to increasing 5 to 6 is (36-25)= 11 , so the best answer will be the mid point i.e 5,5 = 50
answered by Veteran (13.6k points)  
0 votes

option c) 52

 

Here , we have constraints x>=4 and y>=4

In order to satisfy the equation x+y >= 10 , we need to have min value of x and y as 4 and 6 .

so , min(x2 + y2) = 16+36 = 52

answered by Boss (5.4k points)  

why B is not the ans

because minimum of min(x+ y2)

Here , we have constraints x>=4 and y>=4

In order to satisfy the equation x+y >= 10 , we need to have min value of x and y as 5 and 5.

so , min(x+ y2) = 25+25 = 50

@Arjun ,

why 52 is answer ? It should be 50.

 

0 votes
x+y≥10   

  2x+3y≥20,

  x≥4,

  y≥4.

 we have to choose that value of x & y which satifies all the equations,

as well as give the min ( x^ 2 + y^ 2) which can be possible when X= 5 and Y=5  , min ( x^ 2 + y^ 2) = 5^2 + 5^2 = 50
answered by Active (1.8k points)  


Top Users May 2017
  1. akash.dinkar12

    3578 Points

  2. pawan kumarln

    2314 Points

  3. Bikram

    1950 Points

  4. Arjun

    1852 Points

  5. sh!va

    1682 Points

  6. Debashish Deka

    1296 Points

  7. Devshree Dubey

    1282 Points

  8. Arunav Khare

    1122 Points

  9. Angkit

    1072 Points

  10. LeenSharma

    1028 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 29 - Jun 04
  1. Arunav Khare

    246 Points

  2. Arjun

    202 Points

  3. pawan kumarln

    108 Points

  4. Rupendra Choudhary

    94 Points

  5. Niharika 1

    90 Points


22,909 questions
29,243 answers
65,403 comments
27,745 users