3 XCELL Printing has created a new cartridge for 3D printers

3. XCELL Printing has created a new cartridge for 3D printers that they claim is far superior to the
closest alternative cartridge sold by MM Printing. XCELL is in the process of selecting a price for
the cartridge and wants to learn what the cartridge will be really worth to customers who are
manufacturing firms. The MM cartridge sells for $200. While the MM cartridge breaks down
with a probability of 40% after every 500 print jobs on a 3D Printer, the XCELL cartridge breaks
down with a probability of 30% after every 900 print jobs. Every fix in case of a breakdown
requires an hour of labor cost and also a material cost of $5. The XCELL cartridge requires a
higher quality plastic compared to the MM cartridge. Suppose you are told that the cost of
plastic amounts to $10 per carton for XCELL and $8 per carton for MM, and typically a customer
would need to reorder a carton every 450 print jobs. Also, you are told that $20 is the hourly
rate for labor hired by the typical manufacturing firm. Also, on the average, a manufacturing
firm does 4500 print jobs in a year. Suppose the lifetime of a cartridge is 1 year. Calculate the
total economic value of the XCELL cartridge.

Solution

Solution:

Price of MM cartridge = $200

Probabiility of break down of MM cartridge = 40% after 500 print jobs

Average print for a manufacturing firm = 4500 print job

Expected breakdown for MM cartiridge = 4500/500*40% = 3.60

Cost of fixing breakdown for MM cartridge = Material cost + labor cost = ($5*3.60) + (3.60 * 1*20) = $90

Probability of breakdown for Xcell cartridge = 30% after every 900 print job

Expected breakdown for Xcell cartridge = 4500/900*30% = 1.50

Cost of fixing breakdown of Xcell Cartridge = (5*1.50) + (1.5*1*20) = $37.50

Required cost of carton for MM Cartrdige = 4500/450*8 = $80

Required cost of carton for Xcell Cartridge = 4500/450*10 = $100

Total economic value of MM cartridge = $200 + $90 + $80 = $370

Total economic value of Xcell Cartridge = $200 + $37.50 + $100 = $337.50