## Problem No.1

The john equipment company estimates its carrying cost at 15% and its ordering cost at $90 per order. The estimated annual requirement is 78,000 units at a price of $4 per unit.

**Required:**

(i). What is the most economical no. of units to order?

(ii). No. of orders to be placed in a year.

(iii). About how often will an order need to be placed?

### Solution

**(i). Economical No. or Units to Order:**

Annual requirement = 48,000 units

Ordering cost = $9 per order

Carrying cost = 15% of per-unit cost.

Per unit cost = $4 per unit

**(ii). No. of orders to be placed in a year:**

= Annual requirement / EOQ

= 48,000 units / 1,200 units

= 40 orders

**(iii). About how often will an order need to be placed (i.e. frequency of orders):**

Frequency of orders = No. of days in one year / No. of orders

= 360 days / 40 orders

= 9 days

## Problem No. 2

Raymond Bro. has been buying a given item in lots of 900 units, which is three months supply. The cost per unit is $12 and the order cost is $16 per order and the carrying cost is 25%.

**Required:**

How much Raymond Bro.can save per year by buying in most economical quantities.

### Solution

**Working: Computation of Annual Requirement:**

As 900 units are three months supply (i.e. consumption), per month requirement is:

Requirement Per Month: 900 units / 3 months = 300 units

Therefore:

Annual requirement = 300 units x 12 months = 3,600 units

**Economic Order Quantity (EOQ):**

No. of Orders = 3,600 units / 900 units

= 4 orders

= 3,600 units / 196 units

= 18 orders approx.

Ordering Cost = 4 orders x $16 per order

= $64

and in case of EOQ:

= 18 orders x $16 per order

= $288

Average Inventory = 900 units / 2

= 450 units

and in case of EOQ:

= 196 units / 2

= 98 units

Carrying cost = $3 x 450 units

= $1,350

and in case of EOQ:

= $3 x 98 units

= $294

Total cost = $64 + $1,350

$1,414

and in case of EOQ:

=$288 + $294

= $582

saving = $1,414 – $582

= $832

## Problem No. 3

A manufacturing company placed an order of 24,000 units semiannually at a price of $20 per unit. Its carryng cost is 15% and the order cost is $12 per order.

**Required:**

(i). What is the most economical order quantity?

(ii). How many orders need to be placed?

### Solution

No. of orders per year = Annual Requirement / EOQ

= 48,000 units / 620 units

= 77 orders approximately

**Computation of Annual Requirement:**

24,000 units are ordered semiannually, therefore:

Annual requirement = 24,000 units x 2 = 48,000 units.

The john equipment company estimates its carrying cost at 15% and its ordering cost at $90 per order. The estimated annual requirement is 78,000 units at a price of $4 per unit.

Required:

(i). What is the most economical no. of units to order?

(ii). No. of orders to be placed in a year.

(iii). About how often will an order need to be placed?

In the question annual requirement is given as 78000. But in answer it is taken as 48000 and the entire answer is wrong I think. Please don’t post such mistakes in publicly posted websites. We trust you and that is why we refer these questions and answers for quick reference. It

EOQ=Square root of (2*78000*9)/(4*15%)

The entire answer is wrong I think.

EOQ=Square root of (2*78000*9)/(4*15%)

= Sqrt (1404000/.6)

=Sqrt (2340000)

=1529.71

Number of orders placed in an year=Annual consumption /EOQ

=78000/1529.71

=50.99

Frequency of orders=Number of days/Number of orders

=365/50.99

=7.16 days

He has just used 48000 in place of 78000, the approach is correct.

A company has an annual demand of 8000 units for an item. The supplier offers the units for sale at $10.00 per unit for orders up to 500 units and at $9.00 per unit for orders of 500 units or more. What is the economic order quantity if the order cost is $30.00 per order and the holding cost rate is 30% per unit cost per year?