Pemodelan Matematika Komponen Model Matematika

Summary

In this video, the presenter walks through the process of creating a mathematical model for a business case involving mango and banana sales. Starting with an influence diagram, they move on to defining the components of the model, including variables like profit, decision variables, and constraints. The presenter explains the use of symbols, units, and values for each component, such as the price and weight of fruit, as well as capacity limits. The goal is to build a mathematical model, which will later be validated and verified, offering a foundation for decision-making in business scenarios.

Takeaways

• 😀 The first step is to create an influence diagram for the case at hand (involving fruits).
• 😀 The next step involves determining the components of the model based on the influence diagram.
• 😀 The outer icons of the diagram (e.g., circles, squares) help identify the key components of the model.
• 😀 Decision variables are represented by boxes, and their values are usually unknown, e.g., the number of mangoes or bananas.
• 😀 Variables must be numeric and represent quantities that can take specific values (e.g., capital, amounts of fruit).
• 😀 A specific symbol is used to represent each component, such as 'X' for unknown decision variables.
• 😀 Parameters are defined, such as the price of mangoes and bananas, with units like rupiah per kilogram.
• 😀 Constraints, like available capital and cart capacity, are represented by icons such as clouds.
• 😀 Each variable has a defined unit, like kilograms for fruit or rupiah for currency, and appropriate symbols for these units.
• 😀 A table summarizing the components of the model, including variables, parameters, values, and units, is created for clarity.
• 😀 After defining the components, the next steps involve constructing the mathematical model and later verifying and validating it.

Q & A

What is the primary focus of the script?

The script focuses on explaining how to create an influence diagram and then move on to constructing a mathematical model, including identifying variables and constraints relevant to a business case involving mangoes and bananas.

What is the first step mentioned in the process?

The first step mentioned in the process is creating an influence diagram, which helps to visually represent the relationships and components of the model.

How does the speaker suggest identifying the components of the model?

The speaker suggests identifying the components of the model by looking at the icons in the influence diagram, specifically the outermost icons like epsilon, clouds, and boxes.

What does 'epsilon' refer to in the context of the model?

'Epsilon' refers to a variable in the model, specifically a value or component that represents profit, with units in 'rupiah' (R) in this context.

How are decision variables represented in the model?

Decision variables are represented using boxes and are symbolized by 'X', indicating they are unknown or mysterious elements that can be controlled or adjusted in the model.

What example variables are used in the model for this case?

The example variables used are the quantities of mangoes (symbolized as X) and bananas (symbolized as Y), with the unit being kilograms.

What is the role of constraints in the model?

Constraints are represented by clouds and restrict the possible values for the variables. For example, the constraints could be the available capital (B1) or the capacity of the cart (B2).

How are the prices and costs associated with the fruits presented?

The script mentions the buying and selling prices of the fruits, such as the buying price of mangoes at 8,000 rupiah per kilogram and the selling price at 9,200 rupiah per kilogram, as well as similar details for bananas.

What is the significance of using 'kg' as the unit of measure for fruits?

Using 'kg' (kilograms) as the unit of measure simplifies the calculation of total weight for the fruits, helping in modeling the business case effectively with clear and consistent measurements.

What is the next step after constructing the influence diagram and identifying the components?

The next step is to construct a table of the model components, detailing each variable, decision, and constraint. This table serves as a standard reference, especially for mathematical modeling and thesis work.