Question

Find two numbers whose product is a maximum when the sum of half the first number and ten times the second number is 100

Answer 1

@gymnast4Jesus<3

Answer 2

Oh, you are not so good in tagging someone.. :P

Answer 3

haha i know im sorry

Answer 4

do you have any idea how to solve this problem?

Answer 5

@gorv wanna continue with Regina??

Answer 6

please i beg. need all the help i can get

Answer 7

only if u r not willing to do it :P

Answer 8

Okay, I am not willing.. :P

Answer 9

:/

Answer 10

What is that simile for??

Answer 11

let first number is =x

Answer 12

what is have so far ir 100=1/2x times 10z

Answer 13

I *

Answer 14

@Regina.D gorv will help you here.. :)

Answer 15

Thank you gorv

Answer 16

second number =y

Answer 17

okay im using x and y

Answer 18

\[\frac{ x }{ 2 }+10*y=100\]

Answer 19

subtarct x/2 both side

Answer 20

okay i subtracted it

Answer 21

10y=100-x/2

Answer 22

divide both side by 10

Answer 23

y=10-x/20

Answer 24

i wrote that

Answer 25

so we got the value of y

Answer 26

so now their product

Answer 27

so now that we have the y value we need x right? since the problem asks for 2 numbers

Answer 28

no x we will keep and replace y with what we got

Answer 29

oh

Answer 30

product= x*(10-x/20)

Answer 31

\[=10x-\frac{ x^2 }{ 20 }\]

Answer 32

we have to maximize it

Answer 33

how do we maximize it?

Answer 34

using differentiation

Answer 35

on differentiation

Answer 36

=10-2*x/20

Answer 37

oh god i dont know how to do that

Answer 38

You can also maximize it by stretching it from both the sides.. :P

Answer 39

my professor is an idiot

Answer 40

u know how to do differentiation

Answer 41

i dont we werent taught it yet which is why im so confused with this problem

Answer 42

This topic of maximize and minimize comes under Differentiation part...

Answer 43

okk..u know anything about differentiation

Answer 44

nothing at all

Answer 45

i just started pre calc

Answer 46

wait

Answer 47

May be there is some other method without using differentiation.. :(

Answer 48

that is why i'm here...because i need help

Answer 49

we can do it using quadratic 's graph but i know that ..but i had prob that i cant make u understand that

Answer 50

@ganeshie8 @hartnn plzz help here..

Answer 51

lol

Answer 52

its not that hard of a problem..

Answer 53

i;m just stupid in math

Answer 54

but you guys will solve it for sure

Answer 55

....................................

Answer 56

alright you guys are all idiots lmao

Answer 57

see ya

Answer 58

We all are idiots here.. :) It is a site for idiots, that's why I think you came here.. :P

Answer 59

@amistre64

Answer 60

May I try now??

Answer 61

loll if u know u can

Answer 62

Let us wait and see what amistre has got in his pocket.. :)

Answer 63

Find two numbers
define the 2 numbers as: x and y

whose product is a maximum
xy is largest when ...

when the sum of half the first number
x/2

and ten times the second number
10y

is 100
x/2 + 10y = 100

Answer 64

Simply find x and y?? :P

Answer 65

all i did was summaraize gorvs procees i believe

Answer 66

no after that..how we will maximise

Answer 67

well, with substitution we get a quadratic ....

Answer 68

bcozz the asker havent done differentiation

Answer 69

yeah with quadratic we will do thta what i said

Answer 70

a vertex is gone over in algebra

Answer 71

but i cant guide him/her so asked for your assistance

Answer 72

i m weak in qudratic graph having max and min prob

Answer 73

Somewhere I read, that for quadratic equation's product to be maximum then it is maximum when :

\(x = \frac{-b}{2a}\)

Answer 74

x/2 + 10y = 100

solve for x (or y, im doing x)

x = 200 - 20y

sub into f = xy

f = (200-20y)y

f = 200y -20y^2

plenty of ways to find the vertex

Answer 75

x and y in my case are just numbers, not necessarily axis names

Answer 76

I mean when product is to maximum, then maximum occurs when :
\[x = \frac{-b}{2a}\]

Answer 77

what part of this is the asker having difficulty with ?

Answer 78

For him or her, it is done upto Product.. after that............

Answer 79

\[P = x y =10x-\frac{ x^2 }{ 20 }\]

Answer 80

my x sub makes a prettier solution process :) but im biased

Answer 81

Wait, after that what you want to do??

Answer 82

You are going to find maxima for f and then all that?? Is that??

Answer 83

By using Differentiation??