Oh my god... I've forgotten how to solve math problems

[imported_DocHolliday]

I haven't done any sort of algebra in the past 5 years and can't figure out how to solve this wee lil problem... yes I know i'm retarded for forgetting how to do this stuff... i guess it's true what they say about not using information. But I sure can prepare a tax return and tell you a gazillion rules about it

Anyway... my problem is that i need to figure out a combination of hours and billable rates for a budget in a proposal to a client. So! There are two constant fees $75 and $100. The third fee can vary between $80-$90. Now the number of hours per person has this range:

$75 between 40-65 hours
$100 between 7-10 hours
and the varying fee can vary between 7-15 hours

These need to be whole hours w/ a total number of hours being between 77 and 83... half hours will have to do if there is no other solution.

total fees need to be $6,850.

I can't believe I've forgotten how to solve a problem like this... oh well... if somebody can solve that for me I'd appreciate... and if you are bored enough an explanation on how you did it since I'd like to remember how.

btw... i wrote this quickly so there might be a problem in there... please point it out like ATOT has a mastery of doing haha

 

[BlueWeasel]

I think you need more information to solve this. What exactly are you looking for?

Basically, you've got 1 equation with 3 unknowns. Are there any maximum/average values to use?....otherwise, you could just calculate various combinations for different fees.

Assume that the maximum # of hours is maxed for the two constant fees, and then determine the rate and hours for the varying fee.

6,850 = (65)($75) - (10)($100) - (X)($80) .... X=12.25 hours @ $80

6,850 = (65)($75) - (10)($100) - (X)($90) .... X=10.80 hours @ $90

 

[imported_DocHolliday]

Im pretty sure that all constraints are in there

 

[imported_DocHolliday]

it's something like this:

75x+(80 through 90)y+100z = 6185

where x is 40-65
y is 7-15
and z is 7-10

 

[imported_DocHolliday]

Originally posted by: BlueWeasel
I think you need more information to solve this. What exactly are you looking for?

Basically, you've got 1 equation with 3 unknowns. Are there any maximum/average values to use?....otherwise, you could just calculate various combinations for different fees.

Assume that the maximum # of hours is maxed for the two constant fees, and then determine the rate and hours for the varying fee.

6,850 = (65)($75) - (10)($100) - (X)($80) .... X=12.25 hours @ $80

6,850 = (65)($75) - (10)($100) - (X)($90) .... X=10.80 hours @ $90

the only problem with those answers is that I need have half hours or whole hours with a huge preference on whole hours

 

[Fenixgoon]

well so far you have:

75 n1 + 100 n2 + (80-90) n3 = 6850

n1 + n2 + n3 = 76-84

 

[PING]

what if the total hours work is between 16-39 does that fall in the variable rate of $80-$90?

hrs.
1-6 = ?
7-10 = $100
7-15 = $80-$90
16-39 = ?
40-65=$75


what's the rule for charging $80-$90 vs. $100 when it's 7 hrs.

 

[imported_DocHolliday]

 

[BlueWeasel]

Originally posted by: DocHolliday

Originally posted by: BlueWeasel
I think you need more information to solve this. What exactly are you looking for?

Basically, you've got 1 equation with 3 unknowns. Are there any maximum/average values to use?....otherwise, you could just calculate various combinations for different fees.

Assume that the maximum # of hours is maxed for the two constant fees, and then determine the rate and hours for the varying fee.

6,850 = (65)($75) - (10)($100) - (X)($80) .... X=12.25 hours @ $80

6,850 = (65)($75) - (10)($100) - (X)($90) .... X=10.80 hours @ $90

the only problem with those answers is that I need have half hours or whole hours with a huge preference on whole hours

Well, since #3 fee can vary, just adjust the hourly fee rate until you get whole or half hours.

 

[CocoGdog]

That's okay. One year, I tutored this girl I liked on Algebra. I don't use Algebra or care for it, but managed to sit through 20+ hrs of tutoring. It was worth it though.. sigh...

 

[imported_DocHolliday]

Originally posted by: PING
what if the total hours work is between 16-39 does that fall in the variable rate of $80-$90?

hrs.
1-6 = ?
7-10 = $100
7-15 = $80-$90
16-39 = ?
40-65=$75


what's the rule for charging $80-$90 vs. $100 when it's 7 hrs.

unfortunately the 16-39 is off limits for anybody :/

the 75 dollar rate is the staff who is doing most of the work, the 80-90 dollar rate is the supervisor of the job, and the 100 dollar rate is the partner, so that's why the hours are allocated the way they are

 

[TStep]

Something has to give doesn't it?

Max charge at:

Partner: 10 hrs @ $100 = $1000
Super 15 hrs @ $90 = $1350
leaving $6850-$2350 or $4,500 @ $75 = 60 hrs bringing the total hours to 85

Edited for new info

 

[BlueWeasel]

Well, it's really a matter of which rates you want to maximize. Obviously, you can't use the maximum number of hours with the highest fee for each case, so which one would you prefer to lower the rate or hours?

 

[imported_DocHolliday]

Originally posted by: TStep
Something has to give doesn't it?

Max charge at:

First 10 hrs @ $100 = $1000
Between hour 10 and 15 @ $90 = $450
leaving $6850-$1450 or $5,400 @ $75 = 72 hrs bringing the total hours to 87

either i'm not reading what your saying correctly, or I am and you are thinking that each variable is a separate time frame of the job and not a different person?

 

[kranky]

How about 60 hours @$75, 10 hours @$100 and 15 hours @$90.
That comes to exactly $6850 but totals 85 hours (one more than your stated limit).

 

[imported_DocHolliday]

Originally posted by: BlueWeasel
Well, it's really a matter of which rates you want to maximize. Obviously, you can't use the maximum number of hours with the highest fee for each case, so which one would you prefer to lower the rate or hours?

I posted the range of hours allowable for each rate, as well as the hourly range for the varying rate which is where I was hoping to solve the problem. the partner rate of 100 and the staff rate of 75 are inflexible

 

[TStep]

Yeah I was looking at a running total of hours, not different classes. Edited post above and you are one hour over (matching Kranky's finding)

 

[imported_DocHolliday]

Originally posted by: kranky
How about 60 hours @$75, 10 hours @$100 and 15 hours @$90.
That comes to exactly $6850 but totals 85 hours (one more than your stated limit).

oo that's close... I'll have to go check, but i'm pretty sure my range on those hours might have been too liberal... it would be best to keep it between 77 and 83... I'll change that in the OP.

is there a solution in this range w/ either whole or half hours?

 

[imported_DocHolliday]

be back in an hour... lunch

 

[TStep]

Lowering the hour limitation is not going to help. Both krnaky and I figured the maximum hrs chargable at the maximum rate and still came up over the hour limit. Somebody's hourly rate has to go up or max hours have to go up.

It's a b!tch backing into a bid, I windup doing price justification all the time.

Edit: or you need to come up with misc fees (ie: printing, misc mat'l, etc) to cover the difference.

 

[kranky]

I don't think there's a solution under 85 hours.

To keep the number of hours lower, you want to maximize the most expensive hours.
So you use all 10 of the $100 hours and all 15 of the variable rate hours, setting the variable rate to the max of $90.

The only variable left is the number of $75 hours and you need 60 to come to $6850. That puts you over the 83 hour limit.

[edit: TStep beat me to it]

 

[imported_DocHolliday]

85 hours was fine! thanks for your help guys (and girls... HAH!)