Question

A local store purchases a 20 ounces jar from a supplier. The store monthly demand is 27000 jars. The holding cost per jar per year is 20 cents and the cost of placing an order is $50. The store operates 20 days per month and 10 months per year. The Manager is currently ordering 8000 jars each time he places an order. How much can the Manager save the store by using the Economic Order Quantity?

Answer 1

$279.415

Step-by-step explanation:

1. Find the Total Cost.

1.a. Calculate the Economic Order Quantity (EOQ).

Theoretically, the EOQ is the optimal order quantity that a firm should purchase in order to minimize its inventory costs (holding costs are included here), and costs of placing an order.

Mathematically:

`EOQ=\sqrt{(2DS)/(H) }`

Where:

D= demand.

S= cost of placing an order.

H= holding cost (per unit and per year).

In the statement, we identify each of these values:

Here we must find the annual demand, therefore, D: 27,000 (monthly demand)*12 = 324,000; S: $50, no operation should be performed; and H: $0.2 (per unit and per year).

We replace in the EOQ equation:

`EOQ=\sqrt{(2(324,000)(50))/(0.2) }`

`EOQ=\sqrt{(32,400,000)/(0.2) }`

`EOQ=√(162,000,000)`

`EOQ=12,727.92`

So, the optimal order quantity equals 12,728.

1.b. Calculate the Total Cost:

To do this, we follow this formula:

`TC=((EOQ)/(2) *H)+((D)/(EOQ) *S)`

We replace the values:

`TC=((12,728)/(2) *0.2)+((324,000)/(12,728) *50)`

`TC=(6,364*0.2)+(25.4557*50)`

`TC=1,272.8+1,272.785`

`TC=2,545.585`

2. Find the Total Cost when order quantity is 8,000 jars.

Now we are going to determine how much the company saves if it only purchases 8000 jars (that is, 4728 units below the ideal quantity).

Again:

`TC=((EOQ)/(2) *H)+((D)/(EOQ) *S)`

We replace the values, but this time EOQ = 8,000.

`TC=((8,000)/(2) *0.2)+((324,000)/(8,000) *50)`

`TC=(4,000*0.2)+(40.5*50)`

`TC=800+2,025`

`TC=2,825`

3. Define the magnitude of the saving.

To do this, we simply subtract the Total Cost with 8,000 units minus the Total Cost with EOQ.

`Saving=2,825-2,545.585`

`Saving=279.415`