My Optimization Problem

I have been playing a classical violin for 9 years now.  I love the soft sound of the wooden instrument, but once I heard Alexander Markov perform on his electric violin (his Paganini Caprices are incredible!), I was hooked.

In that moment, I resolved to get an electric violin for myself.  So for the past two years, I have been saving up my money. I used every opportunity to make money, from working around the house doing laundry and folding it, to washing our cars, vacuuming, watering the garden, helping with cooking, doing dishes, and tutoring my sister.  Finally this past week, after adding up all my birthday money, graduation gifts and the rest of my savings, I had a total of $330.

I woke up all excited but then realized that I had never bought anything so expensive before.  I had no idea where to start.  I got even more confused when I did a Google search for “electric violin sale.” and got over 225,000 results! I clearly needed a plan, so  I asked my dad for some advice and he suggested that I follow these steps:

1. Figure out what my budget was (and what my bottom price is)
2. Identify the violin and amplifier models in my price range
3. Find at least 3 vendors that sell these exact items
4. Call each one to verify the package price and availability
5. Compare all 3 vendors and their prices and find the best deal 

He cautioned me that each different vendor will deliberately try to confuse me by changing their packages slightly (making some items appear cheaper but charging a higher price for others.  This was an optimization problem. I would need to take my time and do my research.  My first step was to create a spreadsheet.  In it, I wrote the store names, the salesmen’s names, his extension number, pricing information for each item, etc.

Before placing my first call, I was both excited and nervous at the same time.  When the representative answered the phone, I felt my heart beating so hard I thought that it was going to jump out of my chest!  After a few seconds of conversation, I got more relaxed and comfortable working from my script.  On my second call, I was already doing much better and even deviated from my script and asked the salesman where he was located.  By the time I got the third vendor, I was enjoying the conversation.   

Name	Name	Phone	Violin	Amp	S&H	Total
Music 123	Rick	888 566 6123	299	49.99	7.44	357.42
Musician's	Jeremy	800 860 4077	299	51.98	8	359.97
Woodwind	Lakisha	800 348 5003	299	59.00	0	358.99

After completing the spreadsheet, I looked it over and discovered that even though I had prices, it was still was quite confusing.  Some vendors quoted lower prices on some items (like the amplifier) but higher prices for others ( like the violin.  In another case, the amplifier was slightly less expensive, but the violin was higher).

The problem was that I couldn't easily calculate the lowest price on any of the packages because they weren't identical.

I decided to select the two lowest price vendors and try to work out their differences.  I called both vendors again and asked them to give me another quote for a specific package, (i.e. just the violin, carrying case, amplifier, and cable).  I deliberately eliminated all the other confusing items like the extended warranty, bow, extra strings, rosin etc.  When I was done with these conversations, I finally had the price of $357.42, which was still $37.42 above my budget.   My very stubborn father and mother refused to budge and pay the difference, so I had to go back to the drawing board.  I figured that maybe I would be able to lower the price a bit more.

I called the last vendor again and told him that I am ready to place an order today, and asked if he would be willing to give me a 10% discount off the package for $322 (which would bring the price down slightly below my budget of $330).  He seemed a bit annoyed, but after 20 seconds of tense silence,  he said that he would.  I said:  “You’ve got yourself a deal!” and I told him that it was a “pleasure doing business with him,” and then I put my dad on the phone so he could complete the transaction for me.

I felt proud of myself and for the rest of the day, I had a big grin on my face. I managed to save up and buy a big ticket item that I had wanted for two years. I did all the research by myself,  I figured out a way to simplify the confusing pricing of the different packages, and I successfully negotiated a price that was below my budget. I went around telling anyone who was willing to listen to my experience…even the mailman! 

Yes, sir-ee, Thursday was a good learning day indeed.