Retail Price optimization Problem Pricing a product is a crucial aspect in any business. Alot of thought process is out into it. There are different strategies to price different kinds of products. There are products whose sales are quite sensitive to their prices and as such a small change in their price can lead to noticeable change in their sales. While there are products whose sales are not much affected by their price - these tend to be either luxury items or necessities (like certain medicines). This notebook will focus on the former type of products.

Price elasticity of demand (Epd), or elasticity, is the degree to which the effective desire for something changes as its price changes. In general, people desire things less as those things become more expensive. However, for some products, the customer's desire could drop sharply even with a little price increase, and for other products, it could stay almost the same even with a big price increase. Economists use the term elasticity to denote this sensitivity to price increases. More precisely, price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant.

Mathematically speaking, the price elasticity of demand is defined to be the percentage change in quantity demanded, q,divided by the percentage change in price, p. The formula for the price elasticity (ǫ) is: e=%ΔQ/%ΔP

In this work, we shall look at the sales of the items of a cafe. This cafe sells burgers, coke, lemonade and coffee. As a data scientist, it is our task to figure out the optimal prices to set for these items. If the price is set too high, the sales will drop & the price is set to low, then the margins will decrease. What is the sweet spot that will give us the maximum profit?