Question

Patterson Electronics supplies microcomputer circuitry to a company that incorporates microprocessors into refrigerators and other home appliances. One of the components has an annual demand of 250 units, and this is constant throughout the year. Carrying cost is estimated to be $1 per unit per year, and the ordering cost is $30 per order.a. To minimize cost, how many units should be ordered each time an order is placed?
b. How many orders per year are needed with the optimal policy?


c. What is the average inventory if costs are minimized?


d. Suppose that the ordering cost is not $30, and B. Brady has been ordering 250 units each time an order is placed. For this order policy (of Q = 250 to be optimal, determine what the ordering cost would have to be.

Answer 1

Answer:

a) Q = 122 units/order

b) Number of orders = 2.05 orders/year

c) Average inventory = 61 units

d) Ordering costs = 125 $/order

Step-by-step explanation:

The economic quantity order (EOQ) formula allow us to minimize the ordering cost, in function of the demand, ordering cost and holding cost.

The EOQ formula is:

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

where:

D: demand in units/year

S: Order costs, per order

H: holding or carrying cost, per unit a year

a) In this case:

D: 250 u/year

S: 30 $/order

H: 1 $/year-unit

$EOQ=\sqrt{\frac{2DS}{H} }=\sqrt{\frac{2*250*30}{1} }=\sqrt{15000}=122.47\approx122$

b) If we have a demand of 250 units/year and we place orders of 122 units, the amount of orders/year is:

$\#orders=\frac{D}{EOQ}=\frac{250\,units/year}{122\,units/order}=2.05\, \frac{orders}{year}$

c) We assume that there is no safety stock, so everytime the stock hits 0 units, a new order enter the inventory.

In this case, the average inventory can be estimated as the average between the inventory when a new order enters the inventory (122 u.) and the inventory right before a order enters (0 u.)

$\#av.inventory=\frac{122+0}{2}=61$

The average inventory is 61 units.

d) If 250 units is the optimal quantity for an order, it means it is equal to the EOQ. We can calculate the new ordering costs as:

$EOQ=\sqrt{\frac{2DS}{H} }=\sqrt{\frac{2*250*S}{1} }=250\\\\2*250*S=250^2\\\\S=250/2=125\,\ /order$

Answer 2

Answer:

Step-by-step explanation:

It depends on how many they want to order at a time if they do 4 orders a year at ordering 65 units each order they will spend $37.25 each order and $149.00 a year or they could buy they whole amount that they are needing for the year say the whole 260 units in one order and spend $86 on one order