Find two positive real numbers whose product is a maximum. (enter your answers as a comma-separated list.) the sum of the first

Question

Natalija [7]

3 years ago

6

Find two positive real numbers whose product is a maximum. (enter your answers as a comma-separated list.) the sum of the first

and three times the second is 54.

Mathematics

1 answer:

Vladimir [108] · Answer 1 · 2022-02-07T23:30:48+03:00

the sum of the first and three times the second is 54.

x + 3y = 54

3y = 54 - x

y= 54 /3 - x / 3 = 18 -x /3

xy = x (18 -x /3) = 18x - x^2 / 3 = - 1/3 x ^ 2 + 18 x


since a<0, it is concave downward, and the vertex is the maximum value. That vertex occurs at x= - b /2a = (-18) / (-2/3) = 12


The first number is x=12.
The second is y = 18 -x /3 = 18- 12/ 3 = 18 - 4 = 14