Pricing Model Formula Based On Units Produced

We are trying to work out a pricing model based on how many units we will produce. In production the price per unit will be really high when you produce a low quanity, and the price per unit will be lower with the more units you produce (but never reach zero). What we are trying to accomplish is to create a formula to build a pricing structure that accounts for this curve without having to price every possible scenario.

For example, if we have the following data where for 1 unit we charge $3 per unit to produce, for 5 units we charge $2 per units to produce, etc...:

1 units @ $3 per unit
5 units @ $2 per unit
10 units @ $1 per unit

What I need to figure out is how much it would cost per unit if we were to produce 3 units. I'm guessing it would be somewhere around the $2.40 mark give or take. Or say 8 units, would be something like $1.50 per unit.

Is there a formula that can calculate this? I've tried thinking of it as a moving average, or prorating the pricing.