relevant costing

A contract requires 10 kg of material X. There are 250 kgs of this material in invenrory which was purchased in error over 2 years ago. If material X is modified, at a cost of $2 per kg, it could then be used as a substitute for material Y which is in regular use and currently costs $6 per kg. Material X could also be sold for a scrap value of $0.50.

-What is the relevant cost?
-The answer is $40.
-According to me if we modify it we will get $4(6-2) but will also have an opportunity cost of $0.50, therefore the relevant cost should be this total.

-In the book it says,”The latter is the preferable option so the relevant cost is $4 per kg for 10 kgs = $40.”

-I have not understood this. Could you explain specially the logic?

Thanks.