SOLUTION: Find 2 positive real numbers whose product is the maximum given that the sum is twice the first and three times the second is 48

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Question 534302: Find 2 positive real numbers whose product is the maximum given that the sum is twice the first and three times the second is 48
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Find 2 positive real numbers whose product is the maximum given that the sum is twice the first and three times the second is 48
:
Two numbers, x & y
:
2x + 3y = 48
3y = -2x + 48
y = -2%2F3x + 16
:
x*y
replace y with (-2%2F3x+16)
write an equation
f(x) = x(-2%2F3x+16)
f(x) = (-2%2F3x^2+16x)
find the axis of symmetry, x = -b/(2a)
x = %28-16%29%2F%282%2A%28-2%2F3%29%29
x = %28-16%29%2F%28-4%2F3%29
x = -16 * -3%2F4
x = +12 gives max on the above equation
:
Find y
2(12) + 3y = 48
3y = 48-24
y = 24/3
y = 8
:
The two real numbers for max xy: 12,8