Having difficulty solving what feels to be an easy problem - Linear equation.

[gusrohar]

I have spent the entire day trying to solve this problem but I haven't come to a conclusion.

There are two offers for a copying machine for a months use with the following limits:

(1) $5000 for 10,000 copies and then 12 cents for any additional copy.
(2) $2000 for 8000 copies and then 25 cents for any additional copy.

How many copies a month do you need to make for (1) to be profitable.

I understand inequalities and have no problem solving them. However I can't seem to make a function out of any of the 2 equations.


If I use y=kx+m the first equation might translate to something like y=0.12x + 5000 but then I haven't really put in any information about the least amount of copies being 10,000.

Any guidelines?

Edit:To clarify, I 'm having trouble making an expression/formula to solve the inequality
Edit: I've thought about a million different ways to make an expression of the given data for both offers. For the first expression lets say y equals the amount of money and x the amount of copies above 10,000. Then y = 5000 + 0.12x. But where do I put the limit of 10,000 copies?

I understand that the k value for x needs to be 0.12 for (1) and 0.25 for (2). Still not getting anywhere in my head.

 

[Deleted member 4993]

I have spent the entire day trying to solve this problem but I haven't come to a conclusion.

There are two offers for a copying machine for a months use with the following limits:

(1) $5000 for 10,000 copies and then 12 cents for any additional copy.
(2) $2000 for 8000 copies and then 25 cents for any additional copy.

How many copies a month do you need to make for (1) to be profitable.

I understand inequalities and have no problem solving them. However I can't seem to make a function out of any of the 2 equations.


If I use y=kx+m the first equation might translate to something like y=0.12x + 5000 but then I haven't really put in any information about the least amount of copies being 10,000.

Any guidelines?

Edit:To clarify, I 'm having trouble making an expression/formula to solve the inequality.

#1 offer:

cost = 5000 for x≤10,000

cost = 5000 + (x - 10000) * 0.12 for x>10000 .....................edited

#2 offer:

cost = 2000 for x≤8000

cost = 2000 + (x - 8000) * 0.25 for x>8000 .....................edited

To start of, assume that the # of copies /month = x > 10000

Then for #1 to be profitable:

5000 + (x -10000) * 0.12 ≤ 2000 + (x - 8000) * 0.25 .....................edited

Now continue......

 

[gusrohar]

First offer:

cost = 5000 for x≤10,000

cost = 5000 + x * 0.12 for x>10000

Second offer:

cost = 2000 for x≤8000

cost = 2000 + x * 0.0.25 for x>8000

To start of assume that the # of copies /month > 10000

Then to be #1 to be profitable:

5000 + x * 0.12 ≤ 2000 + x * 0.0.25

Now continue......

Alright so for the equation to make any sense I need to assume that the only x values allowed are above 10,000. I think that was my problem, trying to solve it for all x values allowed. Thank you!

 

[Deleted member 4993]

#1 offer:

cost = 5000 for x≤10,000

cost = 5000 + (x - 10000) * 0.12 for x>10000 .....................edited

#2 offer:

cost = 2000 for x≤8000

cost = 2000 + (x - 8000) * 0.25 for x>8000.....................edited

To start of, assume that the # of copies /month = x > 10000

Then for #1 to be profitable:

5000 + (x -10000) * 0.12 ≤ 2000 + (x - 8000) * 0.25 .....................edited


Now continue......

.

Please look at my EDITs above

 

[gusrohar]

What is your logic behind:

cost = 5000 for x≤10,000

cost = 5000 + (x - 10000) * 0.12 for x>10000

Edit:Nevermind just understood