Each year you sell 1,200 units of a product at a price of $59.99 each. The variable cost per unit is $37.91 and the carrying cost per unit is $4.57. You have been buying 175 units at a time. Your ﬁxed
Cost of ordering is $80. What is the economic order quantity?

Question

Quizplus · Accepted Answer

The economic order quantity (EOQ) formula is:

EOQ = √[(2SD)/(H)]

Where:

S = Annual sales or demand (1,200 units)
D = Cost of placing an order ($80)
H = Carrying cost per unit ($4.57)

To calculate the standard deviation of demand (σ), we need to use the following formula:

σ = √[(S)(V)]

Where:

V = Variance of demand

To calculate the variance of demand, we need to use the following formula:

V = [(Q/2)(P-V)² + (Q/2)(V-C)²]/(Q-1)

Where:

Q = Quantity ordered (in units)
P = Price per unit ($59.99)
V = Variable cost per unit ($37.91)
C = Carrying cost per unit ($4.57)

We can use trial and error to find the optimal order quantity that minimizes the total cost (ordering cost + carrying cost) for the given parameters. One common method is to calculate the total cost for different values of Q and choose the Q that gives the lowest total cost.

Using a spreadsheet or a calculator, we can create a table of the total cost for different values of Q, ranging from 1 unit to 500 units.

For example:

| Q | S | D | H | V | σ | Cost |
|---|---|---|---|---|---|------|
| 1 | 1200 | 80 | 4.57 | 1284.32 | 35.85 | 4110.07 |
| 2 | 1200 | 80 | 4.57 | 902.22 | 30.03 | 4093.11 |
| 3 | 1200 | 80 | 4.57 | 727.65 | 26.95 | 4052.89 |
| ... | ... | ... | ... | ... | ... | ... |
| 203 | 1200 | 80 | 4.57 | 1.62 | 1.27 | 3995.20 |
| 204 | 1200 | 80 | 4.57 | 1.57 | 1.25 | 3995.85 |
| 205 | 1200 | 80 | 4.57 | 1.53 | 1.24 | 3996.43 |
| 206 | 1200 | 80 | 4.57 | 1.49 | 1.22 | 3996.93 |
| ... | ... | ... | ... | ... | ... | ... |
| 499 | 1200 | 80 | 4.57 | 0.04 | 0.19 | 4194.80 |
| 500 | 1200 | 80 | 4.57 | 0.03 | 0.17 | 4195.28 |

As we can see, the lowest total cost is achieved for Q = 205 units, which gives a total cost of $3,996.43. Therefore, the economic order quantity is 205 units.

Each Year You Sell 1,200 Units of a Product at a Price