Question

For product M, a firm has an annual holding cost percentage of 20%, an ordering cost of $80 per order, and annual demand of 10,000 units. If they order less than 1100 units at a time, the purchase price is $10.00. If they order 1100 or more units, then the purchase price for all units is only $8.00. How much should the firm order at one time? The correct Answer is 1,100. Please show me how to come up with this answer. Show work and give explanation.

Answer 1

Comparing Total cost at EOQ = 895 and Q = 1100 . we find that the total cost is minimum at Q =1100. Therefore firm should order 1100 or more.

Step-by-step explanation:

Annual Demand = 10,000 units

Ordering cost = $80

Holding Cost = 20% = 0.2

less than 1100 price $10

more than 1100 price $8

EOQ when p = $10

EOQ = sqrt((2 * 10,000 * 80) / (0.2*10)) = 894.43 = 895 units

Total Cost at EOQ

TC = (Annual demand * Unit price) +((Annual demand / Quantity) * Ordering cost) + (( Quantity / 2 ) * Holding rate * Unit Price)

TC = (10,000 * 10) + ((10,000 / 895) * 80) + ((895/2) * (0.2 * 10) = $1,01,788.85

Now for ordered quantity 1100 or more

TC at Q = 1100

TC = (10,000 * 8) + ((10,000 / 1100) * 80) + ((1100/2) * (0.2 * 8) = $81607.27

Comparing Total cost at EOQ = 895 and Q = 1100 . we find that the total cost is minimum at Q =1100. Therefore firm should order 1100 or more.