Question

Ivonne Callen sells beauty supplies. Her annual demand for a particular skin lotion is 1,000 units. The cost of placing an order is $100, while the holding cost per unit per year is 20% of the cost. This item currently cost $50 if the order quantity is less than 100. For orders between 100 and 399 units, the unit cost falls to $49. For orders of 400 units or more, the unit cost falls to $48. To minimize total Inventory cost:

(1) How many units should Ivonne order each time she places an order?

(2) What is the minimum annual total cost? Show work.

Answer 1

Demand, D 1000

Cost of ordering, k 100

h 20%

EOQ = sqrt(2*D*k/(h*P))

Slabs Price, P EOQ Q* Ordering Cost Inventory Cost Purchase Cost Total

<100 50 141.42 99.00 1010.10 495.00 50000.00 51505.10

100-399 49 142.86 142.86 700.00 700.00 49000.00 50400.00

>=400 48 144.34 400.00 250.00 1920.00 48000.00 50170.00

1) Optimal order quantity is 400

2) Total minimum cost is 50170.00