Discount Calculation from a Range - math

Question

Discount Calculation:
Product quantity and range
1 - 10 - 1%
11 - 20 - 2%
21 - 30 - 3%
31 - 40 - 4%
41 - 50 - 5%
the above are the quantity range and their discount% given,
for example:
each product cost is 100
if i purchase 50 product then 5% discount is 250
Now if i purchase 50 products at 2 terms let say 20 and 30 then
for 20 product 2% discount = 40
for 30 product 3% discount = 90
total discount = 130
but here i have to get discount as 250,
Problem description:
the product can be purchased in n number of terms for the maximum quantity, here maximum quantity is 50. discount% for the purchased product is given from the above range. when total discount is added it should be equal. here when 50 product is purchased 250 is given as discount same 250 should be total discount even when product purchased as 20, 10, 10 in terms or 25, 25 whatever.....
plz help me with the calculation part, with some formula or anything....

Answer 1

I assume that you want the discount rate to always increase as the number of purchased items increases, and if that's the case, there's no way to do this.
Here's the logic. The basic equation is:
n1d1 + n2d2 + n3d3 = (n1 + n2 + n3)dx
One obvious solution to this is to have all the d's being equal, that is, all the discount rates are the same. Otherwise, there's no general solution (that is, no set of d's that will work for all n combinations -- for example, whenever all but one of the n's are zero then the d's on both sides of the equation will have to be the same, so the only general solution is that all d's are the same), and if you want a specific solution with different d's, you could solve for the correct value of d given a set of n's, but when you do that, it's clear if one of the d's is smaller than dx, another will have to be larger, so you can't have an strictly increasing discount rate.

Answer 2

Calculate the discount for the previous item count. (How much discount has been given before.)
Calculate the discount for the new item count (previous + current order). (How much discount the customer should have.)
Give a final discount as the difference between the two values.
Store the new item count (of each type) for the customer to some database.
float SimpleDiscount(float cost, int count)
{
if (count <= 0) return 0;
if (count <= 10) return 0.01f * cost;
if (count <= 20) return 0.02f * cost;
if (count <= 30) return 0.03f * cost;
if (count <= 40) return 0.04f * cost;
return 0.05f * cost; // count > 40
}
float GetDiscount(int customerId, int itemId, int count)
{
float cost = GetItemCost(itemId);
int previousCount = GetCustomerOrderedItemCount(customerId, itemId);
float previousDiscount = SimpleDiscount(cost, previousCount);
int newCount = previousCount + count;
float newDiscount = SimpleDiscount(cost, newCount);
SaveCustomerOrderedItemCount(customerId, itemId, newCount);
return newDiscount - previousDiscount;
}
For example:
Item cost = 100
For 20 items: Discount = 40 (2%)
For 30 items: Discount = 210 (7%)
Total discount = 250 (5%)