I found a new apartment that I’m in love with, and I’m moving at the beginning of May. I called two moving companies which had been recommended to me to get price estimates.

Both will send 3 people.

Company A charges $100/hr for their services. However, they have a 2.5 hour minimum charge. They also charge $100 for 1 hour of travel time (30 minutes to the apartment and 30 minutes from the apartment). There is an additional fee of $50 for packing charges for my futon, mattress, and TV. Lastly, they charge by the quarter hour. So if they worked 151 minutes, they’d charge me for 2.75 hours.

Company B charges $130/hr for their services. They have a 2 hour minimum charge. They also charge a travel fee, but it is only $65 in total. Lastly, they too charge by the quarter hour. So if they worked 121 minutes, they’d charge me for 2.25 hours.

The question I was left with is: which is the better company for me to hire?

The only variable is the amount of time the movers spend moving.

The x-axis is the hours spent moving, the y-axis is the amount of money my bank account will be missing. Company A is in blue, Company B is in red.

What’s awesome is that we just taught functions and function transformations in my Algebra II class. And one of the functions we worked with a lot was the floor (step) function. We’ve also talked about piecewise functions. If I were teaching an accelerated class, I would literally give them the information and ask them to (a) first produce the graph,  and then (b) from the graph, come up with a function that gives them the graph.

They’re going to have to recognize they’ll need a piecewise equation, and then also have to figure out how to make the function transformations on the step function to get the second half of the piecewise equation.

I kind of love this problem.