the following question. In the BFDA step 2, the last step that we did not complete, how many constraints are there?

Well, now we want to introduce the first kind of analysis we're going to do. We're going to call this analysis using deterministic optimization models. So deterministic, we think we have good single estimates of all the properties of our situation. Optimization, we're going to build models where we can work within to find the best solution to the model.

So this kind of model that we're going to introduce here and talk about is called linear programming model or linear programming models, and it's one of the more commonly used models that you'll see in business. And essentially, it's a model where all of the relationships, all the mathematical relationships that we think exist in the real situation, are linear. And that's obviously part of the name-- linear programming model. All of the relationship layers-- there's no x squared value to the formula that you think that describes the situation or anything else, just a variable raised to the first power, the linear. And programming comes-- just another word for planning. These are often planning models where all the relationships are linear.

And we want to demonstrate this with a case. And the name of the company here that we want to talk about and show linear programming model is called WinDoor. It's a glass company. So what we want to do here is we want to step through this Business Framework for Decision Analysis, BFDA. We already defined this once, but we want to now actually use it. And when we build a model, we're going to build a linear programming model.

OK, so let's get started here. And let's take a look at this case. And so it's, as you see here, the WinDoor Glass Company. They produce high-quality windows and glass doors. They have three plants or three kind of parts of their production that are organized plant. And they call it plant 1, 2, and 3, and here's what they do.

And they have some new products that-- of course, they're constantly working on new products, but they have two new products that are kind of ready to go to market. We think they're going to be good products and they're going to capture some part of the market. And they also see that some of their existing products are declining in sales a little bit, so they have some production capacity that they can apply to these new products.

So as you see here, one's new glass door and one's a new window. And it says the company situation now being addressed is, should the company go ahead with these two new products? And if the answer is yes, what should the production mix or how many of each should we produce and start to bring to the market is what they're kind of talking about and trying to decide at this point.

And it says that, in the discussion, what they've agreed to so far is that they want to begin the production of these using the available unused production capacity that they have and have agreed that they want to make a production that's the most profitable of these two new products. And they want to consider all the alternatives, either all of one or all the other, some mix. And they've gathered some data and here it is-- plant 1, 2, and 3. Here's the new door. Here's the new window.

So you see here in the last column here is how many hours per week they have available to apply to these two new products. And here are the production requirements. So to make a door, one of these new doors, it takes an hour in plant 1 in three hours in plant 3. To make one of the new windows, it takes-- it doesn't take any-- we don't use plant 1. But then we use two hours of plant 2 and two hours of plant [? 1. ?]

So this is kind of a description of the production process that we have for these two new products and here is the available capacity that we can apply. And then also we have an estimate of what the production cost and bringing it to market would cost and all that, and what the revenue we would get for each of these. And here's our profit contribution per door and per window that we've estimated.

So we work for WinDoor and we're asked to help them in this situation. So what we're going to do is we're going to go through this business framework for decision analysis. So let's first state the business issue, just in a few words what is this analysis about. And you ought to be able to do that. It's production. Let's see. There I am. I think I got my caps on here. Production of new products with available capacity. Maybe-- let's see. We're talking per week. We could say weekly production. This is not too important, just kind of to identify the broad area that we're going to do some analysis in.

But now let's go to step 2, and we want to be as specific and clear as we can here because now we want to define very carefully the situation we want to build the model for and do some analysis and get some answers. So the first thing we're asked is, what is the business question? So what is the business question here? Can we state in one sentence what the question is here?

Well, if we go through here, maybe you already got a sense of what that business question is. But it says here they want to launch these two new products. We want to start to produce them. And we even say, what is the production mix, they said. They could do a mix of one or the other, or some combination of the two is what we said down here, all alternatives.

So what's the question here? Something like, what is a good production plan for the these new products? Maybe that's a question mark. Maybe we say what's the production-- maybe we say weekly because all the data came to us in week. Maybe we say, what's a good weekly production plan for these two new products? We could say, with the available production capacity.

So this-- we don't put everything in this, but just a top level, what is that business question that we want to answer? We want to do some analysis and be able to say, hey, here's a good weekly production plan.

So the second part of this business definition is, what's a decision here and how many values represent a decision? Well, I think if we carefully saw this, there are two new products. And we want to know how many of each, how many units of each, how many doors, how many windows. So the number values here is 2, so let's be real clear about this. So it's the number of doors per week and number of windows per week.

So two value. If I tell you four and four, that's a production plan-- four new doors, four new windows. This may seem obvious in this case, but it's not always obvious what, specifically, is a decision here and how many quantitative values represent that decision.

Now, the third thing we want to identify clearly is the objective measure. So in this kind of modeling, linear programming modeling, we need to focus on one objective measure. And so can we find out, in this case, do we have information about what is the objective measure that the organization wants to focus on to help us decide and compare alternative production plans?

Well, I think we go over here, we see that we gathered profit contribution for one door and one window. And up here I said, I think we see that what the executives agreed on is they want to begin production with a mix that is most profitable. So there is the information we need. The objective measure is, we might say, total profit. We could say per week. And we could say the measure is going to be dollars. So as we're looking at different production plans in this case, this organization, these executives say, we want to choose a good production plan and good to us means profit, a high value of profit.

So we've gone through three of the elements here to kind of carefully define a problem situation that we want to do modeling and analysis for. The final element is the constraints. What are the constraints that we want to make sure are taken into account when we consider different production plans? So we're going to stop here and ask you to think about what are the constraints. How many are there and what are they that we need to take into account for this situation?

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