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Tomtit [17]
2 years ago
10

Write the number 270 as a sum of three numbers so that the sum of the products taken two at a time is a maximum. (Enter the thre

e numbers as a comma-separated list.)
Mathematics
1 answer:
iren [92.7K]2 years ago
3 0

Answer:

x=y=z=90.

Step-by-step explanation:

let the 3 numbers be x,y,z.

let s be sum

s=x+y+z

we need to maximize xy+yz+zx

or , xy + y(270-(x+y))+x(270-(x+y)) = P(x)

Use Lagrange's Multipliers

⇒ΔP= λΔS

⇒\frac{x+y}{x+z} =1

⇒y=x

⇒\frac{x+z}{x+y} =1

⇒z=y

⇒x=y=z

⇒3x = 270

⇒x= 90

hence, x=y=z=90.

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