Variation questions

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christy

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A computer company develops a new scan disk. The cost $P of producing a scan disk is partly constant and partly varies inversely as the total number of scan disks N produced.
When 2500 scan disks are produced, the total cost is $225000. When 5000 scan disks are produced, the total cost is $425000.
(a) Find the cost of producing a scan disk if 2500 scan disks are produced.
(b) Express P in terms of N.
(c) If the selling price of a scan dish is $120, find the profit percentage if the company produces and sells 1000 scan disks.
(d) If the selling price of a scan dish is $100, what is the minimum number of disks that need to be produced in order to make a profit?≠


I have solved part a, this is my answer: 225000/2500 =90
I have trouble in part b, i write this equation but i cannot get the answer : P=c+ k1/N (c,k1≠0)
I think if I can solve part b, I am able to solve part c and d as well.
Thank you.
 
Last edited:


So you understand that it is P(N) = c+k/N for some c,k?


We have P(2500) = 225000 and P(5000)=425000.

Plug then into the formula for P(N). You will have a system of two linear equations in two unknowns and can solve for c,k.
 
daon2 said:


So you understand that it is P(N) = c+k/N for some c,k?


We have P(2500) = 225000 and P(5000)=425000.

Plug then into the formula for P(N). You will have a system of two linear equations in two unknowns and can solve for c,k.
Click to expand...


Sub P=225000 and N=2500
225000=c+ k1/2500
k1=562500000-2500c ---(1)
Sub P=425000 and N=5000
425000=c+ k1/5000
k1=2125000000-5000c ---(2)

Sub (1) into (2),
562500000-2500c=2125000000-5000c
2500c=1562500000
c=625000
Sub c=625000 into (1)
k1=-1000000000

how come i got the answer like this????
 
christy said:
Sub P=225000 and N=2500
225000=c+ k1/2500
k1=562500000-2500c ---(1)
Sub P=425000 and N=5000
425000=c+ k1/5000
k1=2125000000-5000c ---(2)

Sub (1) into (2),
562500000-2500c=2125000000-5000c
2500c=1562500000
c=625000
Sub c=625000 into (1)
k1=-1000000000

how come i got the answer like this????
Click to expand...

Your work is correct. So the Price function is:

P(N) = 6.25*105 - 109/N

As you can see from here - to keep P(N) positive, N ≥ 1600
 
christy said:
but the answer is P=81+ 25000/N
Click to expand...

If that is true then:

P(2500) = 81 + 10 = 91

and

P(5000) = 81 + 5 = 86

In that case:

either you have error/s in your original post

or you are looking at the wrong answer.
 
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