Problem 2 A company based in Oman is faced with the problem of determining the optimal production plan to fulfill customer demand over the next N weeks at the lowest possible cost. The company has M factories, each with its production capacities for both regular and overtime production. Costs associated with regular production and overtime vary by both the factory and the week. Besides its internal production capacity, the company has the flexibility to subcontract, procuring products from S suppliers, and the purchasing costs fluctuate from week to week. The company also manages W warehouses, each incurring a unique holding cost per unit per week, and these costs vary across warehouses. The objective is to minimize the overall cost, encompassing regular and overtime production costs, subcontracting expenses, and warehouse holding costs, all while ensuring customer demand is met.