A manufacturing firm is considering four locations for a new plant. They have collected information on fixed and variable costs for the $4$ potential plant locations. $(8$ points$)$

Location Fixed cost Per unit costs

Material Variable labor Variable overhead

A $$250,000$ $$4$ $$3$ $$4$

B $$100,000$ $$8$ $$10$ $$14$

C $$150,000$ $$5$ $$7$ $$8$

D $$200,000$ $$8$ $$12$ $$15$

a$)$ Plot the total cost curves for the four plant locations on a single graph. $($You may take a picture and attach it$)$

b$)$ Find the break$-$even points and determine the range of demand for which each location has a cost advantage.

c$)$ Which plant location is best if demand is $8,000$ units?