Question

A manufacture has been selling 1150 television sets a week at 480 dollars each. A market survey indicates that for each 12 -dollar rebate offered to a buyer, the number of sets sold will increase by 120 per week.
a) Find the demand function p(x), where x is the number of the television sets sold per week, assuming that p(x) is linear.
p(x)=
b) How large of a rebate should the company offer to a buyer, in order to maximize its revenue?
c) If the weekly cost function is 92000 + 160 x, how should it set the size of the rebate to maximize its profit?

Answer 1

?

Answer 2

help any one

Answer 3

P(x) = - x/10 + 115 + 480
= - x/10 + 595

Answer 4

why x/10?

Answer 5

slope = -12/120

Answer 6

ok so what would be the demand func?

Answer 7

P(x) = = - x/10 + 595

Answer 8

Now can you find Revenue func?

Answer 9

im trying

Answer 10

can u please explain how u got p(x)

Answer 11

x = quantity of TV set, y = unit price
=> (x, y ) = ( 1,150, 480 )

Answer 12

y - 480 = (- 1/10 ) ( x - 1,150 )

Answer 13

Can you do the calculation?

Answer 14

are u finding the eq of the line?

Answer 15

"assuming that p(x) is linear"

Answer 16

ok now i understood the whole equation of the line...

Answer 17

so how would i solve part b?

Answer 18

R(x)

Answer 19

ok

Answer 20

would R(X) be P(X)*x?

Answer 21

You just has responded to me in the very previous post like that :)

Answer 22

lol

Answer 23

i suck at math...

Answer 24

At first you need to master the business concept, otherwise i give up :(

Answer 25

ok so this what i got for R(x)=(-x*(x-5950))/(10)

Answer 26

Multiply it out, will you!

Answer 27

(-x^2+5950)/(10)

Answer 28

R(x) = -x²/ 10 + 595

Answer 29

What the problem want you to find?

Answer 30

How large of a rebate should the company offer to a buyer, in order to maximize its revenue?

Answer 31

R(x) = -x²/ 10 + 595 should = max revenue

Answer 32

How to find max?

Answer 33

R(x) = -x²/ 10 + 595 is the rq for max R

Answer 34

eq*

Answer 35

R'(x) = ...

Answer 36

R(x) = -x²/ 10 + 595x

Answer 37

any ideas on how to calc the rebate?

Answer 38

They says find R'(x)

Answer 39

R'(x) = 595-(x/5)

Answer 40

Set R'(x) = 0 ==> x = ..

Answer 41

x= 2975

Answer 42

but this is not the amt for reabte ? so what now ?

Answer 43

$12 rebate --> 120 set TV

Answer 44

x= 2975 is the number of tv sets solf to max revenue?

Answer 45

I think multiply by 1/10 ~ $298 rebate!

Answer 46

no thats not it :(

Answer 47

What the result?

Answer 48

i dont know what the result is ::(

Answer 49

So how do you know it's not $298?

Answer 50

ok if 12rebate = 120 tv sets and x= 2975, then divide 2975/120 and mulitply by 12

Answer 51

this gives us 297.5 or 298 and my hw says this is wrong some how

Answer 52

my hw is online btw

Answer 53

Can you post the sample, so I can have the idea?

Answer 54

A manufacture has been selling 1150 television sets a week at 480 dollars each. A market survey indicates that for each 12 -dollar rebate offered to a buyer, the number of sets sold will increase by 120 per week.
a) Find the demand function p(x), where x is the number of the television sets sold per week, assuming that p(x) is linear.
p(x)=
b) How large of a rebate should the company offer to a buyer, in order to maximize its revenue?
c) If the weekly cost function is 92000 + 160 x, how should it set the size of the rebate to maximize its profit?

Answer 55

thats the entire problem as it is from the website

Answer 56

i dont have any other sample...sorry

Answer 57

You should learn the debate topic before having the homework, right?

Answer 58

yes but this problem is tricky

Answer 59

ok i got the rebate ...its 182.5/ after trying several attempts to solve it ..

Answer 60

Let me think !

Answer 61

Yep, you're right :D

Answer 62

ok great team work

Answer 63

now can u help me with part c???

Answer 64

Hey, you're not suck at math! I believe so ;)

Answer 65

lol ok thanks...but u have been a great help too

Answer 66

The proof is whatever I ask, you can respond smoothly :)

Answer 67

lol ok

Answer 68

Now, what is Profit?

Answer 69

profit = revenue - cost

Answer 70

Put them into the func, will you!

Answer 71

Trust me, if you're suck at math, you already run away from me :P

Answer 72

ok a function would be ((x^2/10)+595x)-(92000+160x)

Answer 73

this calculates to be (x^2/10)+775x-92000

Answer 74

Then maximize profit means ...

Answer 75

Actually,
P(x) = - x²/ 10 + 435x - 9,200

Answer 76

Hey, where ARE you?

Answer 77

im here

Answer 78

just trying to figure it out

Answer 79

Just take derivative P'(x)

Answer 80

ok lets see

Answer 81

= 755-(x/5)

Answer 82

P(x) = - x²/ 10 + 435x - 9,200

Answer 83

= 755-(x/5) is the derivative

Answer 84

Your calculation of Profit func is incorrect!

Answer 85

o no

Answer 86

Just fix the subtraction 595x - 160x = 435x

Answer 87

x/5+755 ...is this correct?

Answer 88

Now take derivative Profit func
P(x) = - x²/ 10 + 435x - 9,200
P '(x) = ...

Answer 89

Exactly what you did for the last b) question!

Answer 90

ok derivative is x/5 +435

Answer 91

x=-2175

Answer 92

P'(x) = - x/5 + 435 = 0 => x = 2,175 units

Answer 93

Now what have you done to get the rebate?

Answer 94

ok 102.5

Answer 95

thats it/ thanks so much for working with me to solve this...

Answer 96

I got $262,5 !

Answer 97

no rebate is 102.5

Answer 98

How do you calculate?