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I seem to be having a problem with writing a general sigma notation for my case.

In this example, I am trying to sell a product on multiple markets (based on the customer's needs), but for each market the customer chooses, he shall get an additional 20% discount.

If he chooses only one market the price is n

If he chooses two markets, the price should be n + n*0.1

Three, n + n*0.1 + n*0.2

Sorry for noob question, help is appreciated

Edit:

Clarification - I am selling a product on five markets. If a customer wants to buy my product, he can choose to do so on all of the five markets. For each market except the first, he will get a +10% discount on the purchase.

Example - Customer decides to buy the product on 4 markets. The price (on one market) is \$1. The customer's price shall then be \$1 (first) + \$0.9 (second) + \$0.8 (third) + \$0.7 (fourth) equaling to $3.4.

Another customer buys the product on 2 markets. The price is also \$1. His final price will be \$1 + \$0.9 = \$1.9

Also it is 10%, and not 20% as noted by Barry Cipra.

lukascobbler
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  • I can give you the summation notation, but I'm not sure I understand the question correctly. Suppose the price for one market is n=$1. Then, according to your formula, the price for two markets is $1.10, and the price for three markets is $1.30. The price is getting higher; how is that a discount? Did you perhaps mean that the price for the second market it $0.90 and the price for the third market is $0.80? – mhwombat Dec 17 '21 at 20:11
  • Yes, that's precisely correct. Sorry for my bad wording – lukascobbler Dec 17 '21 at 21:02
  • It's still confusing. If I choose three markets, do I then pay $0.80 for products for all of the markets? Or do I pay $1.00 for products in the first market, $0.90 for products in the second market, and $0.80 for products in the third market? If it's the latter, then how do you decide which market is "first", which is "second" and so on. As a buyer, I'd want the third market to be whichever I'm ordering the most products for, as that gives me the lowest price. But that might change from one order to the next. – mhwombat Dec 17 '21 at 21:10
  • And if there are 11 markets, are the products in the 11th market free? If there are more than 11 markets, do you start paying people to order products? – mhwombat Dec 17 '21 at 21:15
  • Uhh, I forgot some details, there can only be up to 5 markets. And for the buyer's choice, there is none lol. If you decide to buy the product on three different markets for example, the product will cost $1.00 on the first, $0.90 on the second and $0.80 on the third. – lukascobbler Dec 17 '21 at 21:21
  • I suspect that wombat is writing an answer; can you edit your question to reflect the clarifications and additional details? – Eric Nathan Stucky Dec 17 '21 at 21:27
  • The expressions you've written don't make a lot of sense (to me, at least); they make it look as if the price is going up, not down, when the customer chooses multiple markets. It might be better to show a made-up example, with some actual dollar amounts, in which customer A chooses one market, B chooses two, and C chooses three. What does each customer wind up paying for their order(s)? – Barry Cipra Dec 17 '21 at 21:55
  • Also, the text talks about an "additional 20% discount" for each market chosen, but other things seem to suggest a 10% change. – Barry Cipra Dec 17 '21 at 22:02
  • I did edit it now, sorry my bad explanations. – lukascobbler Dec 17 '21 at 22:17

1 Answers1

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Let $p$ be the base price for the product.

Assume the customer orders $n_1$ products for the first market, $n_2$ products for the second market, and so on, up to $n_N$ products for the $N$th market ($N \le 5$). The amount you invoice them for is

$p \sum_{i=1}^N n_i \frac{11-i}{10}$

Ex: $p=\$7$, $N=3$, $n_1=5, n_2=4, n_3=2$. The total is

$7 * (5*1.00 + 4*0.90 + 2*0.80) \approx \$71.40$

mhwombat
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