# Percentage contribution to utilization rate or negative change by grouped units

I have (I'll use some made-up numbers) 100 units, and I can calculate an utilization rate for each. It's done by calculating first (number of days in the month)*(capacity of unit), so let's say 31*20 = 620 (=$$y_1$$). Then I calculate how many days there were customers present, let's say, 580 (=$$x_1$$), so utilization rate would be $$\frac {580}{620}$$ = 94%. Total utilization rate over all 100 units is calculated with $$\frac {(x_1 + x_2 + ... + x_{100})}{(y_1 + y_2 + ... + y_{100})}$$ = 87%. I can't change this.

I've classified the units into three different groups A, B, and C:

A = utilization rate less than 70% (40 units)
B = utilization 70-90% (50 units)
C = utilization rate over 90% (10 units)

Now I should find out how much each group contributes to the total company wide utilization rate of 87%.

I have the specific days when customers were present and the capacities of each unit available, but I can't wrap my head around the calculation itself. I'd like most to show the contribution of each unit to the "drop" from 100% (e.g., group A contributed a drop of - xx ppt from 100%, group B of -yy ppt and group C of -zz ppt, totalling a drop of 100-87 = 13 ppt.) If this was just a single number the contribution would be easy to calculate, but as the utilization rate consists of two different "components", I'm lost. Any ideas on how to calculate this correctly?

• Use LaTeX please. – Michael Rozenberg Jun 25 at 12:51
• Better now? I added some spaces and TeX markings. – KatS Jun 25 at 13:27