Question

Parts purchased from a distributor cost $20 each, and demand forecast for next year is 1,000 units. If each time an order is placed the cost is $5 and the storage cost is $4 per unit per year, what quantity should be ordered each time? It is requested: 1. What quantity should be ordered on each occasion? 2. What is the total order cost for that year? 3. What is the total storage cost for that year?

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Answer to a math question Parts purchased from a distributor cost $20 each, and demand forecast for next year is 1,000 units. If each time an order is placed the cost is $5 and the storage cost is $4 per unit per year, what quantity should be ordered each time? It is requested: 1. What quantity should be ordered on each occasion? 2. What is the total order cost for that year? 3. What is the total storage cost for that year?

Expert avatar
Birdie
4.5
98 Answers
1. Para determinar la cantidad óptima que se debe pedir en cada ocasión, podemos utilizar la fórmula del Lote Económico de Pedido (EOQ por sus siglas en inglés):

EOQ = \sqrt{\frac{2DS}{H}}

Donde:
D = 1,000 (demanda anual),
S = $5 (costo de realizar un pedido),
H = $4 (costo de almacenamiento por unidad al año).

Sustituyendo los valores en la fórmula:

EOQ = \sqrt{\frac{2 \times 1,000 \times 5}{4}} = \sqrt{2,500} = 50

Por lo tanto, la cantidad óptima que se debe pedir en cada ocasión es de 50 unidades.

2. Para calcular el costo total de pedido para ese año, podemos utilizar la fórmula:

Costo\ de\ pedido = \frac{D}{EOQ} \times S

Sustituyendo los valores conocidos:

Costo\ de\ pedido = \frac{1,000}{50} \times 5 = 20 \times 5 = $100

Por lo tanto, el costo total de pedido para ese año es de $100.

3. Para calcular el costo total de almacenamiento para ese año, podemos utilizar la fórmula:

Costo\ de\ almacenamiento = \frac{Q}{2} \times H

Donde Q = EOQ = 50.

Sustituyendo los valores:

Costo\ de\ almacenamiento = \frac{50}{2} \times 4 = 25 \times 4 = $100

Por lo tanto, el costo total de almacenamiento para ese año es de $100.

\textbf{Respuestas:}
1. La cantidad que se debe pedir en cada ocasión es de 50 unidades.
2. El costo total de pedido para ese año es de $100.
3. El costo total de almacenamiento para ese año es de $100.

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