Photo printing has become an important service offering of many storefront pharmacies today. Customers can upload digital photo files in a variety for formats and request standard prints of 4x6, 5x7, or 8x10 size and expect to pick up their prints within an hour at their local store. The service is a profit center for most storefront pharmacies and also brings in patrons who typically purchase other products during their visit.

Digiprinter Services is in the business of repairing the type of intermediate-sized photo printing equipment present in most storefront pharmacies. The equipment operates mostly automatically as photo files are forwarded to it electronically, but at times the equipment breaks down and requires service. There’s a strong imperative to get malfunctioning printing equipment back in service quickly, and Digiprinter signs service contracts with pharmacy chains to repair failed equipment promptly. As the pharmacies are all 24/7 operations Digiprinter must also have a technician on call 24/7.

In one particular metropolitan area Digiprinter has 57 photo printing machines under service contracts. The equipment is typically reliable and on average suffers a breakdown only once each 30 days. However, when service is called for the time to dispatch Digiprinter’s technician for the area and work on the equipment will typically require 4 hours. Though Digiprinter is a 24/7 operation it only has one technician available at any given time.

Given this information determine the following:

a. Once a service call is made, how long on average (in hours) will a machine in a pharmacy be out of service?

b. Digiprinter has an opportunity to take on more service contracts. However, management doesn’t want to have more than one technician on staff. Additionally, there’s an imperative to keep the average time a photo machine will be out of service to under 10 hours. How many more machines could be put under contract given these restrictions?