Help in finding the simplified formula of a tiered fare

38 Views Asked by At

Please help me find the simplest formula in getting the fare. I can get the fare using layman's calculation (i don't know if that is the correct term) but what I need is a formula. I'm stuck with what I did and I thought that this is the best place to get help. I think it's best to explain this is through example. So,

Problem: Find fare of passenger who will travel a total distance of 12km.

Tiered Fare Matrix:

                        | TIER 0 | TIER 1 | TIER 2 | TIER 3 | TIER n
incremental distance (m)| 1000   | 3000   | 3000   | 3000   | dn
              rate ($/m)| 0.2    | 3      | 2.5    | 2      | rn

where,

TIER 0 is the lowest tier or the starting point

$m$ = meters

$r$ = rate

$d$ = distance

dn = ${d_n}$ = nth distance

rn = $r_n$ = nth rate