Determine which factories to operate and the optimal way to distribute products from these factories to customers in order to minimize the total costs, comprising both fixed operational costs and variable transportation costs. 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.
Question 1
A company must decide which of its factories to keep operational and how to distribute its products from these factories to various customers. The goal is to minimize the total costs, which include the fixed costs of operating each factory and the transportation costs, while ensuring that the demand of each customer is met.
Given Data:
Factories (with production capacities and fixed operating costs):
Factory 1 (F1): Capacity = 500 units, Fixed Cost = $10,000
Factory 2 (F2): Capacity = 400 units, Fixed Cost = $8,000
Factory 3 (F3): Capacity = 600 units, Fixed Cost = $12,000
Customers (with demand):
Customer A: Demand = 300 units
Customer B: Demand = 350 units
Customer C: Demand = 250 units
Customer D: Demand = 200 units
Transportation Costs (per unit) from Factories to Customers:
Customer A Customer B Customer C Customer D
F1 $2 $3 $2.5 $4
F2 $3 $2.5 $3 $2
F3 $2.5 $3.5 $2 $3
Objective:
Determine which factories to operate and the optimal way to distribute products from these factories to customers in order to minimize the total costs, comprising both fixed operational costs and variable transportation costs.
- 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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