However, I would like to contend (or at least hope) that my business training has not all been wasted. In fact, I think in many ways it has prepared me for life has a home manager. There have been the more obvious benefits, such as being able to work in a team setting, knowing how to deal with highly pressurized situations, knowing how to handle requests from multiple parties simultaneously, and being able to function at a normal level on very little sleep. All of these skills were honed in business school, and I am grateful for the preparedness that gave me for motherhood.
But I also find myself thinking in business language for some of my daily activities as well. For instance, I use the thinking behind the Critical Fractile ratio when doing my “inventory planning” (i.e. shopping for household supplies). I often find myself weighing the cost and/or probability of under-stocking versus the cost of over-stocking… It’s been a very useful model for me.
And this past week I’ve been earnestly trying to determine an equation for the Productivity Function of our household. As time goes on, our fight against entropy in this house has seen shifts in the various players within our family unit. Some of the players have been very negative contributors to the positive productivity in our home (i.e. they are “destructors”) at certain times, and then, over time, they have started to migrate into the net positive territory. For example, when Strider was a toddler, he was a great destructor, and therefore, his net contribution to our family productivity was quite negative. Now, however, he is capable of being quite helpful around the house—helps with the dishes, laundry, vacuuming, etc., so his net contribution has become positive. In the intervening years, though, we have obviously had 2 other players born into the family who quickly evolved into net destructors, and Strider’s positive pull has been negated by the destructiveness of these others. As Rayna is growing in skills, though, her contribution is heading towards the positive field as well……..
So as I graphed it out, here are the individual productivity functions of the various players:
**
Now obviously our total productivity as a unit will be a summation of these individual lines, so should look something like this:
And all of this has led me to think: In what year is our minimum point in this Productivity Function? And have we already hit it? Or is the worse yet to come? Knowing that calculus can help us find these optimization points, I just need to fully identify the equation, and then can start taking derivatives. This, however, is the point where I am stuck. I know based on the shape of the curve that there will be several variables, and some of them will be squared…. But I’m not quite sure what they all are. Obviously the logical variables are number of kids, and ages of said kids, but I’m still not sure how to define it. Can anyone help?
I figure this equation will be of great use once it is finalized. For instance, this might be able to show us how many more gray hairs I will get if we add another child to this unit. Also, it could help determine allowances/wages for the players based on their contribution. Another benefit would be the help this equation would provide in budgeting for cleaning supplies in the future. Or, I could use it to forecast our future maximum point in the productivity curve, and schedule a nice long vacation for that time. On second thought, maybe the best time for a vacation would be at a minimum point.
And surely this concept and customizable equation will be marketable, right?
See, Wake Forest? My education did not go to waste.
**You will notice that my productivity level is graphed at a higher level than Pete’s. This is purely a function of time spent inside the home. You will also notice that over time the positive contribution for both adults is seen with a decreasing rate over the years. This is due to the quickly fading mental capacities and energy levels of said adults.
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