A company will manufacture a product for the next four months: March, April, May, and June. The demands for each month are $520,720,520,$ and $620$ units, respectively. The company has a steady workforce of $10$ employees but can meet fluctuating production needs by hiring and firing in any month are $$200$ and $$400$ per worker,

respectively. A permanent worker can produce $12$ units per month, and a temporary worker, lacking comparable experience, only produce $10$ units per month. The company can produce more than needed in any month and carry the surplus over to a succeeding month at a holding cost of $$50$ per unit per month. Develop an optimal

hiring$/$firing policy for the company over the four$-$month planning horizon.

Solve it in GAMS