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 Repair function
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directorz
New Member

USA
2 Posts

Posted - 10/21/2007 :  09:09:28  Show Profile  Reply with Quote
Hello experts,

Suppose an appliance repair tech charges $42 for a service call and $36 per hour for each hour worked, based on increments of 20 minutes rounded up for any time over the increment.

I need to write the function that can be used to calculate a bill for a customer. The only thing I see is X = 42 + 36Y. Problem is I donít see where the increment comes into play. Can someone help?

Thank you
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 10/22/2007 :  07:35:21  Show Profile  Reply with Quote
The solution involves the ceiling function.
See http://en.wikipedia.org/wiki/Floor_function
Since I can't write the correct symbol, I will just use [ ] instead.
First, directorz, X = 42 + 36Y should have been written
as B = 36h + 42 where "B" is the amount of the bill and "h" is the number of hours the repairman worked. Of course, X and Y could have been used but, even then, it would have been more appropriate to write it as Y = 42 + 36X since "Y" is usually the dependent variable and "X" independent.
In any case, that is not the correct solution since this problem needs the ceiling function (read the above link) because it states to "round up" for anything over the increment.
Since it wants the increments in 20 minutes, convert the rate from "$36 per hour" to "$12 per twenty minutes" (because there are 3 sets of 20 minutes per hour, $12 per 20min is the same as $36/hour).
Using the variable "m" for "number of minutes", the ceiling of m/20 (denoted as [m/20] ) produces the following:
m=1 gives [1/20]=1
m=2 gives [2/20]=1
m=3 gives [3/20]=1
m=4 gives [4/20]=1
and so on to
m=18 gives [18/20]=1
m=19 gives [19/20]=1
m=20 gives [20/20]=1
m=21 gives [21/20]=2
m=22 gives [22/20]=2
So, you see, it gives the "number of sets of 20 minutes".
In other words, for 1 minute, it is 1 twenty minute period charge, for 2 minutes, it is still 1 twenty minute charge... When you get to 21 minutes, you start charging for a second 20 minute period.
The solution to the problem would be:
B = 12[m/20] + 42
Again, note that the symbol used should have been

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not
___ ___
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since I don't know what code to put in to get the correct symbol. At one time, a list of codes was posted but I think that topic was archived long ago.

Edited by - the_hill1962 on 10/22/2007 07:59:42
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directorz
New Member

USA
2 Posts

Posted - 10/27/2007 :  08:52:58  Show Profile  Reply with Quote
the_hill,

Thank you for the response. The explanation escaped me but you made it quite clear.
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