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Bonus Question $(20$ points$)$:

You are an operations manager for an e$-$commerce company with warehouses located in different regions. You want to reduce the differences in the inventory levels across these warehouses, ensuring a balanced stock distribution.

Consider the following scenario:

You have three warehouses, and you denote their stock levels by and respectively.

The average stock level $($target stock level$)$ across these warehouses should be $300$ units.

The company aims to minimize the absolute deviations between the stock levels of each warehouse and the target stock level of $300$ units.

Your goal is to balance the stock by minimizing the sum of the absolute deviations from the target stock level, subject to the following constraints:

The total stock across all three warehouses should be between $850$ and $950$ units.

For operational feasibility, the stock at each warehouse should not deviate more than $100$ units from the target stock level of $300$ units.

The difference in stock levels between any two warehouses should not exceed $80$ units.

Question:

Formulate this problem as a linear programming model by linearizing the absolute value terms. Provide the corresponding linear programming problem.

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