Question

Ford and gm carry spare parts for their dealers at a third-party warehouse in the gta area. demand for ford spare parts is 210 units per month, whereas demand for gm parts is 310 per month. each spare part costs $100, and the holding cost is 30% for ford and 25% for gm. currently each company uses a separate truck to ship these parts. each truck has a fixed cost of $500 for ford and $450 for gm. what is the optimal order quantity for ford? what is the optimal order quantity for gm? what is the total annual cost of both companies combined? a third-party provider has offered to combine shipments for each of the two companies one a single truck. this will increase the cost of each truck to $650. if the two companies agree on the joint shipment, what is the optimal lot size for ford? what is the optimal lot size for gm? what is the total annual cost for both companies combined when shipping jointly?

Answer 1

The optimal order quantity for Ford and GM can be computed using the EOQ formula, with costs and demands specific to each. When combining shipments, the EOQ and total annual costs for each company need to be recalculated. The EOQ helps minimize the sum of holding and ordering costs for spare parts inventory management.

Step-by-step explanation:

The optimal order quantity for each company can be calculated using the Economic Order Quantity (EOQ) model. The EOQ model aims to minimize the total cost, which includes both holding costs and order costs. For Ford, with a demand of 210 units per month, a holding cost of 30% of the spare part cost ($100), and a fixed truck cost of $500, the EOQ is calculated using the formula:

EOQ = sqrt((2 * Demand * Order cost) / Holding_cost_rate)

For GM, with a demand of 310 units per month, a holding cost of 25% of the spare part cost ($100), and a fixed truck cost of $450, the EOQ is similarly calculated.

When combining shipments in a single truck with a cost of $650, the optimal lot size for each company would be recalculated taking into account the combined costs, demands, and holding costs.

The total annual cost for both companies combined when shipping jointly would include the combined order costs for a single truck shipment and the holding costs for both Ford and GM spare parts.