Analytics Exercise $4-01$ to $4-07($Algo$)$ Cumulative Units Produced

Units produced data was obtain from quarterly financial statements. Cumulative production is calculated by summing the

production in each quarter. The quarter production days is an estimate of the number of actual production days each quarter of the

year $($weekends and holidays are not included$).$ Note the assumption that production only occurs about $260$ days per year $(465)$

with the model and that this represents about $1\mathrm{.}25$ years of $(325260)$ data.

The column Average Days per Unit is the average speed of the production line through the period shown on each line. For

example, as of the end of $2017-$Q$3,$ a car was completed every $0\mathrm{.}325$ days on average $($assuming the line was running $24$ hours

each production day$).$ The daily production rate is the inverse of this number, for example, $0\mathrm{.}325$ days per unit converts to about

$3\mathrm{.}08$ unit per day.

The graph shows the cumulative average time to produce each car in days. The learning curve equation was obtained by fitting a

trendline line $($with the "Power" option$)$ to the data in Excel $($select the "Power," Display Equation on chart, and Display R$-$squared

value on chart$).$

To answer this first question, duplicate the graph, including the Power curve, and table in Excel as shown previously.

Note: Round your "Average Days per Unit $(y{)}^{?}$ to $9$ decimal places.

Using the equation obtained in question $1,$ calculate how long your analysis indicates that it took to produce the first unit.

Note: Round your answers to $3$ decimal places.

Dars $($K$)$ estimate tne ieamang percent associated witn your equation oy tirst caicurating tne time to procuce the $\frac{?}{{?}_{?}}$ no$,4$ tn$,$ atn, and iotn units.

Using these data, estimate the leaming percent.

Note; Round your answers to $9$ decimal places.

It is possible to obtain these learning curve parameters directly from the fitted Power equation. As you can see, the time for the first

unit is the $K$ in the Power equation

$rx=kx$

where

$x=$ Unit number

$Y_x=$ Days to produce the $x$ unit

$K=$ Days to produce the first unit

$n=logblog2$ where $b=$ Learning percentage

Note that the learning percentage $($b$)$ can be calculated from the exponent using the Excel function $={10}^{n^{*}log(2)}.$ For the

cumulative function $xYx=$xoc$=Kx$ the lesrning percentage $($b$)$ can be calculated from the exponent using the Excel function $=$

$10*((n-1)*log(2)).$

Answer this question by showing the calculations to verify these parameters.

Note: Round your answers to $9$ decimal places. Negative amounts should be indicated by a minus sign. Using your spreadsheet, estimate how long $($in years$)$ it should have

One interesting manufacturing story in recent history relates to Tesla's Model $3.$ The car was introduced on March $31,2016,$ and by July

$2017,$ over $466,000$ reservations had been taken for the car. Actual production started in the third quarter of $2017$ when $260$ cars were

produced. At this point, the race was on to produce as many cars as possible and turn Tesla into a profitable company.

Using data from Tesla's quarterly reports, it is possible to perform an analysis of the revenue and cost of their cars. Starting with late

$2016$ and through $2019.$ Tesla's reports tracked the number of cars sold across their entire product line. The company delivered the

Model S$,$ X$,$ and $3$ during this period, and they reported the total revenue, cost of goods sold, and aggregate number of cars delivered

for each quarter. By simply dividing the revenue and cost by the cars delivered, a rough idea of the relative profitability can be seen in

the following graph.

Tesla initially had a strategy of producing only the high$-$end models that sold for over $$100,000$ per car. As the Model $3$ volume

increased in late $2017$ and $2018,$ revenue per car dropped. It is interesting how the gap between average revenue per car and average

cost per car stabilized in early $2018.$

In this exercise, you will analyze Tesla's Model $3$ production learning curve. The initial goal is to estimate the Model $3\text{'}$s production

learning curve. Next, you will estimate how long it should have taken Tesla to work through that $466,000-$reservation backlog that

existed in July $2017.$ Tesla has said that less than $20$ percent of those reservations were canceled.

Required:

Begin your analysis by plotting how long it took to produce each car versus the cumulative units produced during the first five

months of production in an Excel spreadsheet. The plot and raw data follow.

Average Davs