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

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) (Show Source): You can put this solution on YOUR website!
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 = x + 16
:
x*y
replace y with (x+16)
write an equation
f(x) = x(x+16)
f(x) = (x^2+16x)
find the axis of symmetry, x = -b/(2a)
x =
x =
x = -16 *
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

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