Question

in another post, MSN gave me a good guide on solving my algebra problem (Calculating bid price from total cost). Now, even though I can calculate it by hand, I’m completely stuck on how to write this in pseudocode or code. Anyone could give me a quick hint? By the way, I want to calculate the bid given the final costs .

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 

Answer 1

The function simplifies to:

                  / 1.02 * bid + 115   bid <   100                   | 1.12 * bid + 105   bid <=  500 final cost(bid) = | 1.02 * bid + 160   bid <= 1000                   | 1.02 * bid + 165   bid <= 3000                   \ 1.02 * bid + 170   otherwise 

If you consider each piece as a separate function, they can be inverted:

bid_a(cost) = (cost - 115) / 1.02 bid_b(cost) = (cost - 105) / 1.12 bid_c(cost) = (cost - 160) / 1.02 bid_d(cost) = (cost - 165) / 1.02 bid_e(cost) = (cost - 170) / 1.02 

If you plug your cost into each function you get an estimated bid value for that range. You must check that this value indeed is within that functions valid range.

Example:

cost = 2000  bid_a(2000) = (2000 - 115) / 1.02 = 1848  Too big! Need to be < 100 bid_b(2000) = (2000 - 105) / 1.12 = 1692  Too big! Need to be <= 500 bid_c(2000) = (2000 - 160) / 1.02 = 1804  Too big! Need to be <= 1000 bid_d(2000) = (2000 - 165) / 1.02 = 1799  Good. It is <= 3000 bid_e(2000) = (2000 - 170) / 1.02 = 1794  Too small! Need to be > 3000  Just to check:  final cost(1799) = 1.02 * 1799 + 165 = 2000   Good! 

Since the original function is strictly increasing, at most one of those functions will give an acceptable value. But for some inputs none of them will give a good value. This is because the original function jumps over those values.

final cost(1000) = 1.02 * 1000 + 160 = 1180 final cost(1001) = 1.02 * 1001 + 165 = 1186 

So no function will give an acceptable value for cost = 1182 for example.