Cost-effective formula required

[Hughesy39]

Good afternoon,

I'll come clean - I'm trying to work out a formula for item enchantment in Minecraft. I'm trying to find a formula to indicate whether it's more cost-effective at purchasing two items that are enchanted at a particular level over one item that is enchanted at the next level up.

To explain, if two Protection I items were bought, they could be combined to make one Protection II item. Conversely, if two Protection II items were bought and combined, they would make one Protection III item, and so on, until an item with the highest Protection value (in the example below, it's level IV) was obtained.

However, one item may not be available, and may never be.​

​

For example, I have this table:

[TABLE="width: 250"]
<tbody>[TR]
[TD]Enchantment Level[/TD]
[TD]Cost[/TD]
[/TR]
[TR]
[TD]Protection I[/TD]
[TD]5[/TD]
[/TR]
[TR]
[TD]Protection II
[/TD]
[TD]do not own[/TD]
[/TR]
[TR]
[TD]Protection III[/TD]
[TD]21[/TD]
[/TR]
[TR]
[TD]Protection IV[/TD]
[TD]45[/TD]
[/TR]
</tbody>[/TABLE]


What I'd like to do is calculate whether purchasing 8 Protection I items (at a cost of 40) and combining them all to obtain a Protection IV item is more cost-effective than purchasing two Protection III items (at a cost of 42) to combine them to Protection IV.

I have other enchantments to calculate, too, which have different enchantment levels (eg, 2 or even 5). So two level-4 enchantments, or 16 level-1, could be combined to make a level 5.

I am going round in circles because I don't know the name of the formula to search for in Google. Please could someone assist?


Thanks in advance,

Rob.

 

[RasGhul]

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