Hahn Manufacturing has been purchasing a key component of one of its products from a local supplier. The current purchase price is $$1600$ per unit. Efforts to standardize parts have succeeded to the point that this same component can now be used in five different products. Annual component usage should increase from $150$ to $800$ units. Management wonders whether it is time to make the component in$-$house, rather than to continue buying it from the supplier. Fixed costs would increase by about $$20,000$ per year for the new equipment and tooling needed. The cost of raw materials and variable overhead would be about $$1200$ per unit, and labor costs would go up by another $$350$ per unit produced.

$1.$ Should Hahn make rather than buy?

$2.$ What is the break$-$even quantity?

Please show any and all work as that is really needed to understand the principles.