Apple Inc. received orders for 205, 215, and 210 units of laptops in September, October, and November respectively. The production line can manufacture a maximum of 200 laptops per month for $300 per laptop on the regular time. They can also produce additional laptops by working overtime at a cost of $325 per laptop. Any unsold laptops at the end of the month will incur a storage cost of $20 per unit. The current inventory at the end of August is 10 laptops.

Formulate a linear programming model that minimizes the total cost.

What if the company decides to keep safety stock at 5 units in September, 20 units in October, and 15 units in November? How is the model changed?

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