taranicolee
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
Delete
Share
This Question is Closed
zordoloom
Best Response
You've already chosen the best response.
0
You still there? Do you need help?
taranicolee
Best Response
You've already chosen the best response.
0
yes please!
zordoloom
Best Response
You've already chosen the best response.
0
Do you know calculus?
taranicolee
Best Response
You've already chosen the best response.
0
well haha i'm in the class right now but not really...
zordoloom
Best Response
You've already chosen the best response.
0
Okay. That's fine.
taranicolee
Best Response
You've already chosen the best response.
0
well are you going to help?(:
zordoloom
Best Response
You've already chosen the best response.
0
Do you want just the answer, or how to get the answer?
taranicolee
Best Response
You've already chosen the best response.
0
how to get it please (:
taranicolee
Best Response
You've already chosen the best response.
0
how to get it please (:
zordoloom
Best Response
You've already chosen the best response.
0
okay.
zordoloom
Best Response
You've already chosen the best response.
0
let x= the first number
let y= the second number
zordoloom
Best Response
You've already chosen the best response.
0
so, x+2y=100.
zordoloom
Best Response
You've already chosen the best response.
0
You are trying to maximize the product yz.
so let z= the product = to xy
zordoloom
Best Response
You've already chosen the best response.
0
Following so far?
taranicolee
Best Response
You've already chosen the best response.
0
yeah(:
zordoloom
Best Response
You've already chosen the best response.
0
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
zordoloom
Best Response
You've already chosen the best response.
0
Now, just find the vertex of that graph using -b/2a
zordoloom
Best Response
You've already chosen the best response.
0
Therefore, the first value is 25 and the second value is 50.
zordoloom
Best Response
You've already chosen the best response.
0
Let me simplify this down a bit, because I was writing out my work which may be a bit confusing.
zordoloom
Best Response
You've already chosen the best response.
0
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.
zordoloom
Best Response
You've already chosen the best response.
0
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)
taranicolee
Best Response
You've already chosen the best response.
0
ohhh wait i get it! thank you!!!! do you have time to help me with another one?(:
zordoloom
Best Response
You've already chosen the best response.
0
P = xy = (100 − 2y)y = 100y − 2y^2
zordoloom
Best Response
You've already chosen the best response.
0
Sure.