Weekly shipments to each warehouse will be: WH1, 100; WH2, 150; WH3, 120; WH4, 150; and WH5, 120.What is the optimal location of the distribution center?

Question

Quizplus · Accepted Answer

To find the optimal location of the distribution center, we need to calculate the weighted center of gravity (WCG). WCG = ((Σ (Xi * Wi)) / ΣWi, where Xi is the x-coordinate of the warehouse and Wi is the weight of the shipment to that warehouse.

Calculating WCG: 
((4.6 * 100) + (4.9 * 150) + (4.4 * 120) + (5.2 * 150) + (5.1 * 120)) / (100 + 150 + 120 + 150 + 120) = 4.968

Therefore, the optimal location of the distribution center is closest to coordinates (5.1, 5.1). Since this is not an option, we choose the closest available option, which is C (5.1, 5.1)

Weekly Shipments to Each Warehouse Will Be: WH1, 100; WH2