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.
Accepted Solution
A:
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