Find the two positive numbers

Question

Find the two positive numbers whose product is 200 so that the sum of one and four times the

other is minimum.

Answer 1

xy = 200

x+4y = minimum

Try a few numbers and see where it goes

20 and 10, nice round numbers

20 + 4(10) = 60

try 5 and 40

40 + 4(5) = 60

200 and 1

200+4(1) = 204

nope, not so good

50 and 4

50 + 4(4) = 66

nope

8 and 25

25+ 4(8) = 57

promising

try two numbers where one is 4 times the other

sqr50 and 4sqr50 about 7.07 and 28.28

their product is about 200

they sum to 4(sqr50) + 4sqr50 = 8sqr50 = about 56.56

go slightly higher than 7.07 or slightly lower and you get a larger sum of 4y+x

I'd go with sqr50 and 4sqr50