Republic Manufacture is planning whether to buy or make a part for its assembly. The initial investment for that part is $$12,000.$ The manufacturing cost per part is $$15.$ A supplier can send the same part for $$20$ with an additional transportation cost of $$250$ to transport $100$ parts. a$.$ Find the breakeven quantity and the total cost at the breakeven point.

b$.$ If the company requires $1,200$ parts, find the breakeven quantity and the total cost at the breakeven point. DON'T USE ANY AI OR CHATGPT, THANK YOU

c$.$ If the requirement is $2,000$ parts, what is the best option? What is the cost saving?