Suppose my office uses ten different kinds of inkjet printers, and as a result I need to maintain inventory of ten different types of ink cartridges. This is a large office, and the average demand for each type of cartridge is 15 cartridges per month. My ordering cost is $10.00 per order, and the carrying cost is $2.00 per cartridge per month. What is the optimal order quantity for the inkjet cartridges? (Note, I will need to be maintaining separate inventories and placing orders for each of the ten different types of cartridges. Assume we are using a Q,R system and the different cartridges will be hitting their order points at different points in time.) What is the total annual ordering plus carrying cost of the inventory system, for all ten items? HINT: Find the optimal order quantity and total cost for one of these cartridges. The total cost for all ten types of cartridge is ten times the cost for one.
Suppose in the problem above I could standardize the printers being used, so that all of the printers in my office all use the same inkjet cartridge. Now, instead of 10 different cartridges each having demand of 15 per month, I have one type of cartridge that experiences demand of 150 cartridges per month. What is the optimal order quantity for this standardized inkjet cartridge? How does the total annual ordering plus carrying cost compare to the total cost from the problem above? Explain.