# Modelling question

1. Mar 2, 2006

### lektor

Hi a few questions i want to check my answers for here,

3. Write down an expression, evaluate the constant of proportionality, and answer the question.
[Remember to work in SI units. Simplify answers to 1 d.p. only.]
(a) The annual cost (C) of running a business is partly constant and partly proportional to the number of employees.
If there are 20 employees, the annual cost is $400000. If there are 25 employees, the annual cost is$470000.
Find the annual cost if there are 18 employees

What is meant by partly constant? how would this be written.

C = kN? or C = kN + c?

2. Mar 2, 2006

### assyrian_77

The second one since I guess you mean a constant by c. The first one is as you can see "fully" proportional.

3. Mar 4, 2006

### lektor

hrmk so finished that question and was hoping for some help on this next one.

In a bookstore, the selling price of a certain dictionary is $x. The total profit ($P) on the sale of the dictionary is partly proportional to the selling price of the dictionary and partly proportional to the square of the selling price of the dictionary. When x = 35, P = 78750; when x = 60, P = 60000.
(a) Express P in term of x.
(b) Find the total profit if the selling price of the dictionary is $65. For a) im not certain but this is my expression, P = ( kx ) + (x^2) + c P = x(k + x) + c with my values of c = 107100 and k = -845 found from info given.. so when x = 65 P = 65(-845+65) + 107100 P =$56400

cheers, any corrections and pointers would be great.

Last edited: Mar 4, 2006
4. Mar 4, 2006

### assyrian_77

It doesn't say partly constant, so why is 'c' in the equation? With a nonzero 'c' in your equation, you would have a profit even if the selling price is zero. No, think about it again. What should the equation be?

5. Mar 5, 2006

### lektor

So in that case it will be

P = x . x^2
P = Kx^3

However when i solve for k the answers are different..

Last edited: Mar 5, 2006
6. Mar 5, 2006

### HallsofIvy

Staff Emeritus
I find the phrasing "partly proportional to the selling price and partly proportional to the square of the selling price" confusing but I'm sure "P= k x (x2)= x3" is not intended since that would simply be "proportional to the cube of the selling price". You were closer with your first idea: P= kx+ (x2)+ c. As Assyrian_77 said, drop the c since nothing is said about a constant- and remember that "proportional to the square of the selling price is "cx2". You don't have a constant of proportionality on the x2.