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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.

Respuesta :

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:

[tex]EOQ=\sqrt{\frac{2DS}{H} }[/tex]

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

[tex]EOQ=\sqrt{\frac{2DS}{H} }=\sqrt{\frac{2*250*30}{1} }=\sqrt{15000}=122.47\approx122[/tex]

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

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

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.)

[tex]\#av.inventory=\frac{122+0}{2}=61[/tex]

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:

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

A) To minimize cost, the number of units that should be ordered each time an order is placed is; 122 units

B) The number of orders per year needed with the optimal policy is; 2 orders per year.

C)  The average inventory if costs are minimized is; 61 units

D) For the order policy of Q = 250 to be optimal, the ordering cost would have to be; $125 per order

The formula for economic quantity order (EOQ) is given as;

EOQ = √(2DS/H)

Where;

  • D is demand rate
  • S is set up costs
  • H is holding cost

We are given;

Annual demand; D = 250 units/year

Holding Cost; H = $1 per unit per year

Set up costs; S = $30 per order

  • A) EOQ here is;

EOQ = √(2 × 250 × 30/1)

EOQ = 122.47

But EOQ has to be a whole number and so we approximate to the nearest whole number to get;

EOQ = 122

  • B) With the optimal policy, the number of orders per year is gotten from the formula;

n = D/EOQ

Plugging in the relevant values gives;

n = 250/122

n = 2.049

But number of orders has to be a whole number. Thus, we approximate to the nearest whole number to get;

n = 2 orders per year

  • C) If costs are minimized, the average inventory is defined as the average between of the inventory when a new order enters and the inventory just before a new order enters.

Before a new order enters the inventory is 0 if we assume that there is no safe stock. Thus;

average inventory = (122 + 0)/2 = 61 units

  • D) We are told that ordering cost is not $30 but Optimal order EOQ is 250 and so;

EOQ = √(2DS/H)

⇒ 250 = √(2 × 250 × S/1)

Square both sides to get;

250² = 500S

S = 250²/500

S = $125 per order

Read more about economic quantity order (EOQ) at; https://brainly.com/question/16395657

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