Today we're gonna discuss prescriptive analytics. And the first thing I would like to do is discuss the differences between prescriptive analytics and descriptive and predictive analytics to which you were exposed in the previous lectures. Descriptive analytics takes data, collects it, and tries to map the data to patterns that you can understand in the data. And predictive analytics try to take the behavior of consumers and predict from their past behavior what they're going to do in the future. What we're going to do with prescriptions is we're going to try to give a recommendation. We're going to try and say given the prediction that we had before and given the description of how consumers interact with let's say companies and with other consumers, can we give a recommendation on what the company needs to do in order to change the behavior of consumers. We will cover four things today. We will cover how to define a prescription problem, or how to define a goal, and what we would like to solve in order to improve the actions of a company. Or define two terms which are the objective of a company, or the goal of a company, and also we will try to look at how a company can optimize. What can a company do in order to reach that goal and what actions can a company do to achieve that goal? Finally we are going to look at models. We're gonna discuss how taking an action connects to the goal of the company and influences that. And towards the end, we're gonna take a very brief introduction into competition, or how companies interact and respond to actions by other companies. The first thing I would like to do is tell you what the problem is. Now, it sounds very vague, so I'm gonna show an example in a few seconds, but by saying a problem, what I would like to say is, I would like to say I need to have a goal. Something I would like to maximize, to optimize, to achieve. And I can achieve this goal by taking actions. Now the way to map how actions influence the goal is called the model. And now let's take a few minutes to take a look at the very, very unique example that actually you've seen in the previous lecture. So the first example I would like to talk about is, how do you find what is the optimal price, or the best price to set, in order to sell the maximum quantity of product. So in the descriptive lecture, Professor Iyengar has shown you before the following demand curve or the following graph. And in this what you can see on the x-axis is the price you set for a product. And on the y-axis, you can see the quantity being sold when you change the price of the product. And as you can see, when you increase the price, the quantity goes down. Now let's try to define an objective or a goal. And the first thing we would like to do is we would like to say how can we sell the most quantity of the product? How can we maximize the quantity of the product being sold, right? In this case, the goal or the objective is just to maximize quantity. The quantity we wanna make it as large as possible. And the action we can take is just a simple action. We can just change the price. We can change the price of the product, increase it or decrease it. And by changing the price, we either encourage or discourage consumers whether to buy or not to buy the product. Finally, we need a model. Now models can be very, very complex, but in this case we already have the model, and the model is basically the graph I showed you two slides ago, and you can also see on the bottom right corner. And the model basically tells us, if we change the price, let's say if we increase the price, by how much did the quantity go down? For example we look at this graph, we can see that setting a price of 1 sold the maximum quantity of the product. And the question is, can we change the price even more to do better? Can we use some sort of prediction or recommendation to give to the company to say, can we increase the quantity sold? And the answer is actually, yes. We may not be able to give money to people to buy the product. We can't actually spend money to get them to buy the product. We can probably give them the product for free. We can actually set the price to be 0. In this case we're taking the regression we've seen before, or kind of extending the line to the left hand side. And then we can see using the regression equation, that if we plug in x=0, which means the price equals 0, we'll get the volume of y of 10.13, which is the maximum quantity we can sell. So, in this example, what I tried to show you is we can change the price to increase or decrease the quantity sold. Our goal was to maximise the quantity we sell, and the model was just the graph and the regression equation that Professor Iyengar had shown you. And I've shown you how finding a lower price increases the quantity.