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
:
Two numbers, x & y
:
2x + 3y = 48
3y = -2x + 48
y = {{{-2/3}}}x + 16
:
x*y
replace y with ({{{-2/3}}}x+16)
write an equation
f(x) = x({{{-2/3}}}x+16)
f(x) = ({{{-2/3}}}x^2+16x)
find the axis of symmetry, x = -b/(2a)
x = {{{(-16)/(2*(-2/3))}}}
x = {{{(-16)/(-4/3)}}}
x = -16 * {{{-3/4}}}
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