Question

can someone explain to me how to find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum

Answer 1

You still there? Do you need help?

Answer 2

yes please!

Answer 3

Do you know calculus?

Answer 4

well haha i'm in the class right now but not really...

Answer 5

Okay. That's fine.

Answer 6

well are you going to help?(:

Answer 7

Do you want just the answer, or how to get the answer?

Answer 8

how to get it please (:

Answer 9

how to get it please (:

Answer 10

okay.

Answer 11

let x= the first number
let y= the second number

Answer 12

so, x+2y=100.

Answer 13

You are trying to maximize the product yz.
so let z= the product = to xy

Answer 14

Following so far?

Answer 15

yeah(:

Answer 16

okay, so solve x+2y=100 for x. x=100-2y
z=xy
z=(100-2y)y
z=y(100-2y)
z=100y-2y^2

Answer 17

Now, just find the vertex of that graph using -b/2a

Answer 18

Therefore, the first value is 25 and the second value is 50.

Answer 19

Let me simplify this down a bit, because I was writing out my work which may be a bit confusing.

Answer 20

So, you have been told that the sum of the first number, twice the second is 100
(I'll use just x and y this time to make things less confusing)

so, x+2y=100.

Answer 21

You are trying to minimize the product, P=xy. So solve the first equation x+2y=100, for x.........x=100-2y. Now substitute this into the product formula ( P=xy)

Answer 22

ohhh wait i get it! thank you!!!! do you have time to help me with another one?(:

Answer 23

P = xy = (100 − 2y)y = 100y − 2y^2

Answer 24

Sure.