AndrewG

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Just a simple little worksheet to see if I have enough propane to heat my house for the rest of the winter.


 

Do I have enough propane for the winter?

NULL

I've taken some measurements from my propane tank throughout the winter.  Now we can use Maple to see if we have enough to last the rest of the winter.

``

a := [["nov 27, 2017", 73.5], ["dec 9, 2017", 72], ["dec 16, 2017", 69], ["dec 31, 2017", 62], ["jan 12, 2018", 60], ["jan 19, 2018", 56], ["jan 26, 2018", 54], ["feb 4,2018", 51]]

[["nov 27, 2017", 73.5], ["dec 9, 2017", 72], ["dec 16, 2017", 69], ["dec 31, 2017", 62], ["jan 12, 2018", 60], ["jan 19, 2018", 56], ["jan 26, 2018", 54], ["feb 4,2018", 51]]

(1)

with(Finance)  ``

pts := [seq([DayCount(a[1, 1], a[i, 1]), a[i, 2]], i = 1 .. nops(a))]

[[0, 73.5], [12, 72], [19, 69], [34, 62], [46, 60], [53, 56], [60, 54], [69, 51]]

(2)

with(plots)

listplot(pts)

 

Adding a 30% and 20% level to the graph.  We probably shouldn't be too worried about the cold in June so DayCount("Nov 27, 2017", "Jun 1, 2018") = 186 we'll extend these reference lines out to 186.

plot({pts, [[0, 20], [186, 20]], [[0, 30], [186, 30]]}, view = [default, 0 .. 80])

 

 

30% is the recommended level your propane company wants you to fill up at.  The technician who installed the tank said 20% is all right.  It's up to you if you want to go to 10% but if you run out of propane the company has to come in and do a leak test on your system which is an added cost you don't want.  So let's predict at what point we need to start worrying about filling up our propane tank.  To do that, of course, all we need is a forecast line.  For that we'll just calculate a best fit.

 

a1 := [seq(DayCount(a[1, 1], a[i, 1]), i = 1 .. nops(a))]

[0, 12, 19, 34, 46, 53, 60, 69]

(3)

a2 := a[() .. (), 2]

[73.5, 72, 69, 62, 60, 56, 54, 51]

(4)

X := convert(a1, Vector)

Y := convert(a2, Vector)

with(Statistics)

L1 := LinearFit([1, x], X, Y, x)

HFloat(74.79237702730747)-HFloat(0.34416046490941915)*x

(5)

Plotting it all together

plot({L1, pts, [[0, 20], [186, 20]], [[0, 30], [186, 30]]}, x = 0 .. 200, y = 0 .. 80, labels = ["Days", ""], tickmarks = [default, [seq(10*i = cat(10*i, "%"), i = 1 .. 8)]])

 

Projecting the line to 30% we get

solve(L1 = 30)

130.1496877

(6)

AdvanceDate(a[1, 1], trunc(solve(L1 = 30)))

Record(monthDay = 6, month = 4, year = 2018, format = "%B %e, %Y", ModulePrint = proc (m) Finance:-FormatDate(m) end proc)

(7)

April is still a bit chilly so maybe if we wait until 20%, of course it's getting warmer all this time so our usage should go down.  

AdvanceDate(a[1, 1], trunc(solve(L1 = 20)))

Record(monthDay = 5, month = (), year = 2018, format = "%B %e, %Y", ModulePrint = proc (m) Finance:-FormatDate(m) end proc)

(8)

It isn't warm enough to turn off the furnace yet but it looks like we'll have enough to get us into the warm months

AdvanceDate(a[1, 1], trunc(solve(L1 = 10)))

Record(monthDay = 3, month = 6, year = 2018, format = "%B %e, %Y", ModulePrint = proc (m) Finance:-FormatDate(m) end proc)

(9)

We'll hit 10% well into late spring and almost right into summer of course it's a rough estimate however it looks like we won't have to fill up during the high price winter season.  I can tell my wife to relax, we should have enough propane for the winter.

 

 

NULL


 

Download Propane_usage-.mw

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