Hi, there!
I’ve just finished giving another online Skype lesson to one of my stu-
dents, the winner of the National Excellence Awards for the EIKEN®
Grade 1 Proficiency Test.
She is one of the online students I don’t have to cheer up in every le-
sson because she is very studious and motivated.
I often ask my students the following questions in my online business
class.
What are your life and passion?
What is your raison d’être?
What do you thrive on?
Those are almost interchangeable questions, and you may ask your
friends or colleagues either of the three alternatives.
You must be willing to know what I thrive on. Well, without a doubt,
family is my first priority. Then what is the second? … I would say it
is to keep posting blogs.
What would have been my raison d’être if I had been asked the same
question while working very hard in a trading company? I might have
answered, “To make a lot of profit for my company,” because as a sa-
les representative overseas, that’s how I find myself motivated to keep
working and committed to my job.
Maximizing profit and motivating myself makes me stay outstanding
in an organization of corporate warriors.
Thus, today, let me give the calculation of maximizing profit a try.
Lose no time in referring to the question below.
ABC company can produce a maximum of 1,800 hi-tech machines in
a year. If they sell \(x\) machines during the year, then their profit, in Ja-
panese yen, is given by,
\(P(x) = 40,000,000 – 450,000x + 900x^{2} – \frac{1}{3}x^3\)
How many machines should they try to sell in order to maximize their
profit?
Let me determine the absolute maximum of the profit function and the
value of \(x\) that will give the absolute maximum.
Take a look at the derivative of the profit function and the critical points
that I need for this problem.
\(P'(x) = – 450,000 + 1,800x – x^{2} = – (x – 300)(x – 1,500) = 0\)
Therefore, \(x = 300, x = 1,500\)
I only need critical points that are in the interval [0, 1,800].
Here are those function evaluations.
\(P(0) = 40,000,000\)
\(P(300) = – 23,000,000\)
\(P(1,500) = 265,000,000\)
\(P(1,800) = 202,000,000\)
From the evaluations above, they will need to sell 1,500 hi-tech machi-
nes to maximize profits.
Money is neither almighty, panacea, nor elixir, but money talks.
Your life will take a different shape once you’ve started to think
about monetizing what you do.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
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【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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