Problem $6$:

Jackson Custom Machine Shop has a contract for $130,000$ units of a new product. Sam Jumper, the owner, has calculated the cost for three process alternatives. Fixed costs will be: for generalpurpose equipment $($GPE$),$ $$150,000$; flexible manufacturing $($FMS$),$ $$350,000$; and dedicated automation $($DA$),$ $$950,000.$ Variable costs will be: GPE, $$10$; FMS$,$ $$8$; and DA$,$ $$6.$

a$)$ Plot the total cost function for each company on the same graph.

b$)$ Which alternative should he choose?

c$)$ Identify the volume ranges where each process should be used.

d$)$ If Jackson Custom Machine is able to convince the customer to renew the contract for another one or two years, what implications does this have for his decision?