Question 511562: Find three positive numbers x, y and z such that the sum of y, z, and 5 times x is equal to 180 and the product of the three numbers is maximum.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find three positive numbers x, y and z such that the sum of y, z, and 5 times x is equal to 180 and the product of the three numbers is maximum.
:
5x + y + z = 180
let y = z
5x + 2z = 180
2z = (180-5x)
divide both sides by 2
z = 90-2.5x
:
x*y*z = m (max value)
we can write it
x*z^2
Replace z with (90-2.5x)
f(x) = x(90-2.5x)^2
Plot this equation, locate the max
Max value when x=12, y=43200
Find y and z
y & Z = 
y * z = 60
:
5(12) = 60 + 60 = 180
:
The three positive even numbers: 12, 60, 60
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