Question

Consider the all-units quantity discount schedule below. The annual demand is 90,000 units, setup cost is $1000 per order, and annual holding cost is 30% of the unit cost. What is the optimal order quantity?

Answer 1

1,690 units will be EOQ

Step-by-step explanation:

Missing information:

Quantity Ordered Price Per Unit

1−499 $ 300

500−999 $ 280

1000−1499 $ 250

1500 and over $ 210

EOQ:

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

D = annual demand 90,000

S= setup cost = ordering cost 1000

H= Holding Cost = variable

We will calcualte the EOQ for each possible unit price and check if it is between the range of that quantity.

The best would be an option for the lower inventory cost so we first try for that one:

Holding Cost: 210 x 30% = 63

`Q_(opt) = \sqrt{(2(90,000)(1,000))/(63)}`

EOQ 1,690

to achieve the unit cost of 210 dollar per unit we need to order above 1,500 units which is the case: This is the optimal solution as provide the lower order and holding cost along with the lower inventory cost.