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QUESTION S HUNTERCO

HunterCo operates five plants that produce tomato sauce, with production capacities specified in Table $6.$ The tomato sauce must be stored at one of three warehouses before being shipped to four different customers. However, due to fluctuating demand and variable transportation costs. HimferConeeds a dynamic distribution plan over a three$-$month planning period.

Customer demand vanes over three months, with monthly demand totals as shown in Table $9.$ HunterCo must meet the cumulative demand for each customer over the three month period.

Each plant has variable monthly production costs due to seasonal changes. Warehousing costs vary monthly as well, and each warehouse has a maximum storage capacity that limits the total volume it can hold at any time.

Warehouses can hold limited inventory to account for monthly fluctuations in demand However, holding inventory incurs a penalty cost, whle urmet dentrand results in ahigher shortage penalty.

Shipping costs from each plant to the warehouses and from warehouses to customers vary monfly based on transportation fuel prices, as shova in Table $7$ and Table $8($Expanded$)$

HunterCo aims to mumize its carbon footprint by limiting the total shipping distance. A carbon credit of $\backslash (2\backslash \%\backslash )$ on the monthly cost is applied if the shipping distance remains below a set threshold.

HunterCo has a fixed monthly budget for production, storage, and shipping The $\backslash (\backslash$mathbb$\{$P$\}\backslash )$ model should ensure total monthly costs remain within budget while maximizing serwice levels.

TABLE $6$ Plant Capacities $($in tons$)$

TABLE $7$: Production and Shipping Costs $($per Ton in Hundreds of Dollars$)$

Kalues in each cell represent monthly costs for each of the three months.

TABLE $8$: Shipping Costs from Warehouses to Customers $($per Ton in Hundreds of Dollars$)$

Walues in each cell represen monthly costs for each of the three manths.

TABLE $9$: Customer Mouthly Demand $($Tons$)$

Formulate a mixed$-$integer programing $($MIP$)$ model that minuzes the total cost over the three$-$month planing period, inchudimg production, storage; inventory hoiding, shortage, and shipping costs. Ensure all customer demand is met across the period while adhering to budget and sustainability constraints.