Ace manufacturer is considering purchasing a semi$-$automatic lathe to produce an item they wish to sell. The fixed cost to purchase the lathe is $$250,000$ and each unit produced by the lathe would have a variable cost of $$300.$ Ace believes that the selling price for each unit would be $5500.$

Questions:

Based on the data given, how many units would Ace need to sell in order to break$-$even? $(5$ points$)$

How many units would Ace need to produce in order to make a profit of $$50$ per unit? $(5$ points$)$

How many units would Ace need to produce in order to make a total profit of $$200,000?(5$ points$)$

If Ace can buy the component from a sub$-$contractor for $$400$ unit, how many units would they require before it becomes more profitable to buy the semi$-$automatic lathe? $(5$ points$)$