A manufacturing company needs to decide whether to open or close each of its three factories based on demand from six customers, production capacities, and fixed operating costs. The total demand from customers exceeds the company's maximum production capacity if all factories are operational. Each factory has a fixed cost associated with opening it and variable transportation costs for shipping products directly to customers. Additionally, there's a penalty cost for every unit of unmet demand. The goal is to minimize the total costs, which include the fixed costs of operating factories, transportation costs, and penalty costs for any unmet demand. Given Data: Factories (with maximum production capacity and fixed costs): F1: 200 units, Fixed Cost = $10,000 F2: 250 units, Fixed Cost = $12,000 F3: 300 units, Fixed Cost = $15,000 Customers (with demand): C1: 150 units C2: 200 units C3: 180 units C4: 160 units C5: 190 units C6: 220 units Penalty Cost per Unit of Unmet Demand: $5 per unit Transportation Costs (per unit) from Factories to Customers: C1 C2 C3 C4 C5 C6 F1 $3 $2 $4 $3 $2 $5 F2 $4 $3 $2 $2 $3 $4 F3 $2 $3 $3 $4 $1 $2 Carefully write the mathematical formulations including the constraints. Using Excel Solver, Minimize the total cost of operating factories, the distribution center, and transporting goods from factories to the DC and then to customers.
A manufacturing company needs to decide whether to open or close each of its three factories based on demand from six customers, production capacities, and fixed operating costs. The total demand from customers exceeds the company's maximum production capacity if all factories are operational. Each factory has a fixed cost associated with opening it and variable transportation costs for shipping products directly to customers. Additionally, there's a penalty cost for every unit of unmet demand. The goal is to minimize the total costs, which include the fixed costs of operating factories, transportation costs, and penalty costs for any unmet demand.
Given Data:
Factories (with maximum production capacity and fixed costs):
F1: 200 units, Fixed Cost = $10,000
F2: 250 units, Fixed Cost = $12,000
F3: 300 units, Fixed Cost = $15,000
Customers (with demand):
C1: 150 units
C2: 200 units
C3: 180 units
C4: 160 units
C5: 190 units
C6: 220 units
Penalty Cost per Unit of Unmet Demand:
$5 per unit
Transportation Costs (per unit) from Factories to Customers:
C1 C2 C3 C4 C5 C6
F1 $3 $2 $4 $3 $2 $5
F2 $4 $3 $2 $2 $3 $4
F3 $2 $3 $3 $4 $1 $2
- Carefully write the mathematical formulations including the constraints.
Using Excel Solver, Minimize the total cost of operating factories, the distribution center, and transporting goods from factories to the DC and then to customers.
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