John Smith has a small farm in San Diego, California, that produces plums. The plums are dried on the

location and sold to a variety of supermarkets. Based on mathematical models, he forecasts that sales over

the next $6$ quarters in thousands of packages will be as follows:

Assume that each worker stays on the job for at least one quarter, and that Smith currently has three

workers on the payroll. He calculates that he will have $18,000$ packages on hand at the end of the current

quarter and wants to keep a safety stock of $9,500$ packages at the end of the sixth quarter. Assume that, on

average, each worker is paid $$21,000$ per quarter and is responsible for producing $32,000$ packages.

Inventory costs are estimated to be $5$ cents per package per quarter, and shortages are not allowed. Based

on the effort of interviewing and training new workers, Farmer Smith estimates that it costs $$600$ for each

worker hired. Severance pay amounts to $$800$ per worker.

a$.$ Determine the level output$/$workforce plan that he will need over the next $6$ quarters.

b$.$ Evaluate the total cost of the plan found in part a$.$