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.
1 answer:
<span>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
</span>xy = x (18 -x /3) = 18x - x^2 / 3 = - 1/3 x ^ 2 + 18 x
<span>
</span><span>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
</span>
<span>The first number is x=12.
The second is y = </span><span>18 -x /3 = 18- 12/ 3 = 18 - 4 = 14 </span>
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