(1) Is it optimai? Explain. 5.9. Poseidon Meter, Inc., makes a variety of water meters. Data for the past year indicate a worker can make, on average, 100 meters per four-week period. The inventory holding cost is computed to be SI per meter per period. Backorders, if allowed, cost about $2 per meter per period. New workers can be hired, at a cost of $1000 per worker, and existing workers can be laid off at a cost of $2000 per worker. Workers are paid $1500 per period. There are currently 10 workers at Poseidon. The forecast for the next four periods is 1200, 1200, 1000, and 1000 meters, respectively. (a) Develop a zero inventory plan for the next four periods. (b) Develop a constant work force plan (no backorders) for the next four periods. (c) Develop a constant work force plan (with no more than 50 backorders allowed) for the next fou: periods. (d) Which plan would you recommend, and why