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Apple Inc. received orders from several retailers for laptop delivery at the end of each of the next 3 months. In September: 205 units, then

Apple Inc. received orders from several retailers for laptop delivery at the end of each of the next 3 months. In September: 205 units, then 215 units in October, and 210 units in November. As estimated, there will be 10 laptops in the inventory at the end of August.

The production line is limited to producing 200 laptops that can be made each month at regular times, and the cost is $300 per laptop. They can work overtime for production at the cost of $325 per laptop. If any laptop is manufactured in a given month but not sold during that month, it will cost $20 to store each laptop and carry it over to the following month.

How to formulate a linear programming model that minimizes the total cost.

When the company keeps safety stock at 5 units in September, 20 units in October, and 15 units in November? How is the model changed?

Apple Inc. has the option to place laptops on backorder for $23 per unit every month. It is mandatory that no backorders remain unfilled by the end of November, and currently, there are no backorders at the end of August. How is the model changed?

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