Half of 23 = 11.5 : is there a half-printer in this organization?
An organisation prints over 240,000 pages per annum. This is done over 23 printers. What does each printer print on average over a year if:
- Half of the printers at 100% capacity
- Quarter of the printers operates at 50% capacity
- Quarter of the printers operates at 25% capacity
The assumption in the example is that all printers have the same capacity. I am looking for a average figure that each printer would output based on the criteria.
I appreciate that 11.5 printers is not something that exists in real life but it should not effect the calculation of the average pages printed per printer.
This is essentially a "weighted" average problem. Let X be the number of pages printed by the printers running at 100% capacity. The the printers at 50% capacity print X/2 pages and those running at 25% capacity print X/4 pages. Let N be the total number of printers. Then N/2 are running at 100% capacity and, together, print XN/2 pages. N/4 are running at 50% capacity and, together, print (X/2)(N/4)= XN/8, pages. N/4 are running at 25% capacity and, together, print (X/4)(N/4)= XN/16 pages.
Putting those all together, XN/2+ Xn/8+ XN/16= 240000.
1/2+ 1/8+ 1/16= 8/16+ 2/16+ 1/16= 11/16 so that says that (11/16)XN= 240000 and so XN= (240000)(16)/11. Calculate that and divide by N= 23 to find X, the average number of pages printed by the printers operating at 100% capacity. Divide that by 2 to find the average number of pages printed by the printers operating at 50% and by 4 to find the average number of pages printed by the printers operating at 25%.
Of course, if you really want a single average for all printers, ignore all of that and just divide 240000 by 23!