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?

255

likes
1273 views

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.

Frequently asked questions (FAQs)
What is the surface area of a rectangular prism with lengths 5cm, 8cm, and 10cm?
+
What is the measure of an angle in radians if it is 50 degrees?
+
What is the maximum value of the function f(x) = 2x^2 + 5x + 3 in the interval [-5, 10]?
+
New questions in Mathematics
The patient is prescribed a course of 30 tablets. The tablets are prescribed “1 tablet twice a day”. How many days does a course of medication last?
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.
Determine the correct value: A company knows that invoices pending collection have a normal distribution with a mean of $1.65 million, with a standard deviation of $0.2 million, then: The probability that an invoice pending collection has an amount that is within more than 2 deviations below the mean, is:
Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.
If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.
find all matrices that commute with the matrix A=[0 1]
6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.
How many square feet of floor area are there in three two-storey apartment houses, each of which is 38 feet wide and 76 feet long?
Estimate the quotient for 3.24 ÷ 82
A function is considered exponential when it has a base with positive values greater than zero and different from one, where the exponent is an unknown. An important characteristic of exponential functions is that they show rapid growth or decay as an independent variable increases or decreases. Given the function 25^(x+3)=125, it is calculated that x has the value of
Calculate the difference between 407 and 27
36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt
To get to a hotel on the hill you have to travel 6 km of uphill road and every kilometer there are 6 sharp curves. Each of the sharp curves is marked by three traffic signs. How many traffic signs are there on the stretch of road that leads to the arbergi?
Solve for B write your answer as a fraction or as a whole number. B-1/7=4
X^3 - x^2 - 4 = 0, what are the values of x?
if y=1/w^2 yw=2-x; find dy/dx
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. Point D lies on AB such that CB = CD Point E lies on AC such that CE= DE Determine angle DEC in terms of X
3(x-4)=156