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. show me how to come up with this answer. show work and give explanation.

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.

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.

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