Expert: Paul Klarreich - 3/11/2009

Question
Hiii!, my name is ajanthana and i`m in gr.11 functions and i reallly am in need of some help! i tried answering the question but i came up with a hundred billion answers and well i`m pretty sure a majority of them are wrong please help me!

the demand function for a new product is p(x )=-4x+42.5 . x is the quantity sold in thousands and p is the price in dollars. there are three different types of machines. The cost function for each machine is shown.

machine a: c(x )=4.1x+92.16
machine b: c(x )=17.9x+19.36
machine c: c(x )=8.8x+55.4

investigate the break even quantities for each machine. Which machine would you recommend to the company?

thankkk you sooo much! : ]

Answer
Questioner:   ajanthana
Category:  Advanced Math
Private:  No
 
Subject:  please helpp me: (
Question:  Hiii!, my name is ajanthana and i`m in gr.11 functions and i reallly am in need of some help! i tried answering the question but i came up with a hundred billion answers and well i`m pretty sure a majority of them are wrong please help me!

the demand function for a new product is p(x )=-4x+42.5 . x is the quantity sold in thousands and p is the price in dollars. there are three different types of machines. The cost function for each machine is shown.

machine a: c(x )=4.1x+92.16
machine b: c(x )=17.9x+19.36
machine c: c(x )=8.8x+55.4

investigate the break even quantities for each machine. Which machine would you recommend to the company?

thankkk you sooo much! : ]
....................................
Here is what you do:

1. Write down in words, just what the demand function MEANS.

2. Write down in words, just what the cost   function MEANS.

3. Write down in words, just what the breakeven point MEANS.

Once you do that, you will find that:

-- there is a revenue function, R(x) = x times p(x).
[JUST WHAT DOES THAT MEAN?]

-- the breakeven point has something to do with the cost and the revenue.

Let's try it for (a):

x p(x) = a(x)   << why do we write this?  What does it mean?

x(-4x+42.5) = 4.1x + 92.16

- 4x^2 + 42.5x = 4.1x + 92.16

0 = 4x^2 - 38.4x + 92.16

That is a quadratic.  Solve it by any method.

0 = 4(x^2 -  9.6x + 23.04)

0 = 4(x -  4.8)^2

x = 4.8
.............................
Other parts:

- 4x^2 + 42.5x = 17.9x + 19.36

4x^2 - 24.6x + 19.36 = 0

4(x^2 - 6.15x + 5.84) = 0

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

- 4x^2 + 42.5x = 8.8x + 55.4

4x^2 - 33.x + 55.4 = 0

The solution and interpretation are up to you and your teacher.