Formula for Determining Cost

Question

I am trying to put together a formula for determining company costs for certain services in-house. A little background: before I arrived, the company outsourced their IT work. Now that I've been hired, for the past year we have tried to get away from outsourcing the work and bring it in-house, thereby saving annuals costs to the company (we're a non-profit, so any money we can save is great).

I will be presenting my case to move our networking in-house. I want to put together a formulaic presentation to prove this will be cost-beneficial to us. However, I want it to be generic so that, in the future, I can apply this same formula to different aspects. I'm working on the definitions for the formula.

Here's what I've worked out so far. I need to make sure it is all correct.

When determining to move from an outsourced managed service to an in-house managed service, initial cost must be determined. In determining this cost, the following must be considered to get an accurate budget:

1. Cost of hardware/software/devices
2. Cost of labor
3. Initial setup time

For the first item in the list, two variables are required to determine total cost, $T$.

Let $D_n = x_n(y_n)$, $x,y \in \mathbb{R}, n \in \mathbb{Z}$, where $x_n$ is the number of needed items and $y_n$ is the cost of a single item. $n$ denotes which item it is (i.e. if two different items with separate y cost exist, n=1 for the first item, n=2 for the second, and so forth).

Here is one of the lines of text in question, as I think it is either not needed or I'm thinking incorrectly:

Let $m \in \mathbb{Z}$ and denote the total number of items.

Continuing:

Example: For the installation of new routers in a facility, one must order 3 routers and 75 ft. of cabling, requiring 25 ft. for each router. Each router is \$75 and each 25 ft. length of cabling is \$5. Then

$x_1 = 3$

$y_1 = 75$

$D_1 = 3(75) = 225$

It follows that $D_2 = \$15.$ Using the summation formula $T = \sum_{n=1}^m(D_n),$

$T = 225 + 15 = \$240.$

I have not written the definitions for Labor and Hours yet because I want to ensure I have correctly written this definition. Once I have correctly defined Cost, the definitions for Labor and Hours follow.

Answer 1

Looks good to me! The only thing I'd say is that m doesn't denote the total number of items to be purchased but rather the number of different items to be purchased (2 in your example).