Q1abc Chocolate Manufacturing Company Needs To Decide On How

Q1abc Chocolate Manufacturing Company Needs To Decide On How Many Cho

Q1abc Chocolate Manufacturing Company Needs To Decide On How Many Cho

Q1) ABC chocolate manufacturing company needs to decide on how many chocolate bars should they produce each month to maximize the company profit. ABC consider two types of chocolate bar ‘dark' and 'salted caramel’. Dark chocolate bar required $20 of raw ingredients and take 2 day to make and salted caramel chocolate bar required $30 of raw ingredients and take 4 working days to make. The profit contribution of each dark chocolate bar is $2 and salted caramel chocolate bar is $5. The Manufacture has capacity of 100,000 working days per month and ingredients budget of $10,000 per month.

Using linear programming modelling for ABC company problem, answer the following questions. a) Identify decision, constraint and result variables, and objective function. b) Represent the model in excel sheet, run the model and show the result. Provide a screenshot of your solution.

Q2) Give the name and a brief discussion of any four major types of models used in DSS?

Q3) Write the differences between Forward Chaining and Backward Chaining also list some suitable application areas for both?

Paper For Above instruction

Introduction

Linear programming (LP) is a crucial mathematical technique used in decision-making, especially for optimizing resource allocation within specified constraints. In the context of the ABC chocolate manufacturing company, LP serves as a tool to maximize profit by determining the optimal number of dark and salted caramel chocolate bars to produce monthly. The problem involves balancing raw ingredients costs, production times, resource capacities, and profit contributions, all of which can be formulated through decision variables, constraints, and an objective function.

Decision Variables

The decision variables in this problem are the number of units to produce for each type of chocolate bar. Let:

  • X = number of dark chocolate bars to produce each month.
  • Y = number of salted caramel chocolate bars to produce each month.

Constraints

The constraints are derived from the available resources and operational limitations:

  1. Raw ingredient cost constraint: The total cost of raw ingredients for both types of chocolates must not exceed the ingredient budget.
  • 20X + 30Y ≤ 10,000
  • Production time constraint: The total production time for both types must not exceed the capacity of 100,000 working days.
    • 2X + 4Y ≤ 100,000
  • Non-negativity constraints: The production quantities cannot be negative.
    • X ≥ 0
    • Y ≥ 0

    Objective Function

    The goal is to maximize profit, which is calculated based on the profit per unit of each type:

    Z = 2X + 5Y

    Linear Programming Model

    Maximize Z = 2X + 5Y
    

    Subject to:
    

    20X + 30Y ≤ 10,000
    

    2X + 4Y ≤ 100,000
    

    X ≥ 0
    

    Y ≥ 0

    Excel Implementation

    In the Excel sheet, decision variables X and Y are set in dedicated cells. The total raw material cost and production time are calculated using formulas based on these cells. The solver tool is configured to maximize the profit cell by changing decision variables while adhering to constraints.

    Running the solver yields the optimal production quantities: X and Y that maximize profit within the given constraints. The exact values depend on the solver's solution based on the input data.

    Discussion of Major DSS Models

    Decision Support Systems (DSS) deploy various models to analyze data and support decision-making. Four major types include:

    1. Sensitivity Analysis Models: Analyze how changes in input variables influence outputs, aiding managers in understanding the robustness of decisions.
    2. Simulation Models: Use computational algorithms to mimic real-world processes, useful in risk assessment and policy testing.
    3. Optimization Models: Find the best solution among alternatives, essential in resource allocation and scheduling.
    4. Forecasting Models: Predict future trends based on historical data, important in inventory management and sales forecasting.

    Differences Between Forward and Backward Chaining

    Forward chaining and backward chaining are inference methods used in expert systems and AI, primarily for rule-based reasoning.

    Forward Chaining

    Begins with available data and applies inference rules to derive new facts until a goal is reached. It’s data-driven and useful in scenarios where data is abundant and the goal is to deduce conclusions from facts.

    Backward Chaining

    Starts with a goal and works backward, searching for rules that can support the goal and verifying if conditions are satisfied to achieve that goal. It’s goal-driven and efficient when specific outcomes or diagnoses are sought.

    Application Areas

    • Forward Chaining: Medical diagnosis, troubleshooting systems, and production rule systems.
    • Backward Chaining: Expert systems for diagnostics, planning systems, and legal reasoning.

    Conclusion

    Both forward and backward chaining have distinct advantages, fitting different problem types. Forward chaining is effective for data-rich environments requiring comprehensive inference, while backward chaining is suited for goal-oriented tasks where results are prioritized. Understanding their differences helps in designing efficient DSS and AI applications tailored to specific decision-making needs.

    References

    • Winston, P. H. (2004). Artificial Intelligence. Third Edition. Addison-Wesley.
    • Turban, E., McLean, E., & Wetherbe, J. (2015). Information Technology for Management. Wiley.
    • Sharda, R., Delen, D., & Turban, E. (2020). Business Intelligence and Analytics. Pearson.
    • Yen, J., & Langseth, H. (2008). Decision Support Systems in Action. Springer.
    • Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338-353.

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