Question: Suppose you are running a small factory manufacturing a product called "X". Each year, you face the quarterly demands of the following (all demands must be met on time): Q1: 800 units of demand Q2: 300 units of demand Q3: 1200 units of demand Q4: 500 units of demand The two main cost factors for your business are; 1) wages for your workers and 2) inventory holding cost. Since you strongly advocate the welfare of your workers, you offer a very generous paid-leave package. Workers are working three consecutive quarters, then receive one quarter of paid leave. For example, a worker may work Q2, Q3 and Q4 of a year; then receive a quarter leave in Q1 of the next year. During a quarter in which a worker works, he or she can produce up to 25 units of Product X. Each worker is paid $1,200 per month, i.e. $3,600 per quarter. At the end of each quarter, an inventory holding cost of $100 per unit of Product X is assessed to your business expenses.

1. Formulate an LP to minimise your yearly cost (labour + holding cost) while meeting all demands of each quarter. To simplify the matter, assume that, at the end of each year, the ending inventory is zero. List any other assumption(s) you have made in your formulation.
2. Use Management Scientist to find the optimal solution.

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