Question

I have to following problem to solve. I have to calculate the bidding price from a total price. For example, a client wants to pay 2000$ as a total price, but from this price, there are added costs:

-usage price which is 10% from the bidding price with a minimum of 10$ and a maximum of 50$

-seller price: 2% from bidding price

-added price: 5$ for a bid between 1 and 500 10$ for a bid between 501 and 1000 15$ for a bid between 1001 and 3000 20$ for a bid over 3000$

-storing cost: 100$

from all this, I have to calculate the bidding price for a total of 2000$, for example. I kind of have no clue of how this can be done. Can anyone give me some hints or pieces of answer of what the algorithm should be?

EDIT: ok I got how to calculate the algebra, now where i’m stuck is how to write the algorithm in code or pseudo-code. Anyone got a hint?

Answer 1

You can express all those costs as a function of the bid price. Generate a giant equation that is the sum of all those functions and solve for a particular final value, e.g.:

usage cost(bid) = PIN(bid*0.10, 10, 50) seller cost(bid) = bid*.02 added cost(bid) = PIN(ceiling(bid/500)*5, 5, 10) + PIN(ceiling((bid - 1000)/2000)*5, 0, 10) storing cost(bid) = 100 

So the final cost is something like:

final cost(bid) = PIN(bid*.1, 10, 50) + pin(ceiling(bid/500)*5, 5, 20) + PIN(ceiling((bid - 1000)/2000)*10, 0, 20) + bid*.02 + 100 + bid 

Solve for a particular value and you’re done.

For example, if you want the total cost to be $2000:

2000 = PIN(bid*.1, 10, 50) + pin(ceiling(bid/500)*5, 5, 10) + PIN(ceiling((bid - 1000)/2000)*5, 0, 10) + bid*.02 + 100 + bid. 

Bid must be at least > 1500 and < 2000, which works out nicely since we can make those PIN sections constant:

2000 = 50 + 10 + 5 + 100 + bid*1.02 1835 = bid*1.02 bid = 1799.0196078431372549019607843137 

The PIN expressions are the hardest to factor out, so you might have to guess a few times until you get something that narrows down the range of bids you want to calculate.