Homework SourseAllUnits and Incremental Units Quantity Discounts Demand for
All-Units and Incremental Units Quantity Discounts
Demand for phones at an on-line retailer is 5,000 per month. The annual inventory carrying rate for the retailer is 25 percent, and the retailer incurs a fixed order cost of $15,000 for each order placed with the supplier in Taiwan. The supplier offers a price of $100 per phone for any order that is strictly less than 5,000 phones in the order, a price of $95 if the order size is greater than or equal to 5,000 but strictly less than 10,000 phones in the order and a price of $90 if the order size is greater than or equal to 10,000.
a) How many phones should the retailer order per replenishment if an all-units discount policy is in effect? And, what is the associated average total annual cost? (The other answers people have given me seem to be wrong. I believe the correct answer to be 10,000 phones and $5.5 million in average total annual cost, but I need the work to go with it.)
b) How many phones should the retailer order per replenishment if an incremental units discount policy is in effect? And, what is the associated average total annual cost? (The other answers people have given me seem to be wrong. I believe the correct answer to be 22,000 phones and $5.9 million in average total annual cost, but I need the work to go with it.)
**NOTE: In your calculations report four digits after the decimal. Do not round until you get to the final answer.**
Solution
total cost if 5000 units are ordered = 100+25+3 (15000/5000) = 128
Total cost if more than 5000 but less than 10000 units are ordered = 95+25 +(15000/9000) = 121.66
total cost if 10000 units are ordered = 90+25+(15000/10000) = 121.50
It is minimum when 10000 units are ordered and hence 10000 units should be ordered.
b) total cost if 5000 units are ordered = 100+25+3 (15000/5000) = 128
Total cost if more than 5000 but less than 10000 units are ordered = 128 for five thousand units and 95+25 for other units = average of 128 and 120 is 124.
total cost if 10000 units are ordered = 125+120 + 90+25 +(15000/10000) = average of three is 121
Hence 10000 units should be ordered as it is giving least cost.
It is minimum when 10000 units are ordered and hence 10000 units should be ordered.
