# 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. [Hint: using excel solver]. 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?

A1) For ABC chocolate manufacturing company, the decision variables would be the number of dark chocolate bars (let’s call it D) and the number of salted caramel chocolate bars (let’s call it C) to produce each month. The constraint variables would be the maximum number of working days available (100,000) and the budget for raw ingredients ($10,000) per month. The objective function would be to maximize the company’s profit.

The objective function can be formulated as:

Maximize Profit = 2D + 5C

The constraints can be formulated as:

1. Raw ingredients cost constraint: 20D + 30C ≤ 10,000

2. Working days constraint: 2D + 4C ≤ 100,000

3. Non-negativity constraint: D, C ≥ 0

A2) There are four major types of models used in Decision Support Systems (DSS):

1. Optimization models: These models aim to find the best solution from a set of possible alternatives, considering constraints and objectives. They use mathematical techniques like linear programming, integer programming, or dynamic programming to optimize decisions. They are commonly used in resource allocation, production planning, and scheduling problems.

2. Simulation models: Simulation models are used to mimic real-world systems and analyze their behavior over time. They capture the dynamic operational aspects of a system and are useful when it is difficult or expensive to experiment with the real system. They are commonly used in manufacturing, logistics, and healthcare to assess the impact of different scenarios and make informed decisions.

3. Forecasting models: Forecasting models use historical data to predict future trends, behavior, or events. They are based on statistical techniques, time series analysis, or machine learning algorithms. Forecasting models are used to estimate demand, sales, market trends, or financial indicators. They play a crucial role in inventory management, supply chain planning, and financial planning.

4. Heuristic models: Heuristic models are rule-based or expert-driven models that provide approximate solutions to complex problems. They prioritize simplicity and speed over optimal solutions. Heuristic models are used in situations where finding an exact solution is challenging, such as routing problems, vehicle scheduling, or portfolio optimization.

A3) Forward chaining and backward chaining are two approaches used in rule-based expert systems:

– Forward chaining starts with the available facts and applies the rules to generate new conclusions or facts. It moves forward until the desired outcome or goal is reached. It is a data-driven approach and is suitable for problems with a large number of rules or complex data structures. Application areas for forward chaining include diagnostic systems, monitoring systems, and decision support systems in healthcare.

– Backward chaining starts with the desired outcome or goal and works backward, applying rules to determine the conditions necessary to achieve the goal. It is a goal-driven approach and is suitable for problems with a small number of rules or where the goal is known upfront. Application areas for backward chaining include troubleshooting systems, legal reasoning systems, and intelligent tutoring systems.

Both forward chaining and backward chaining are used in knowledge-based systems to derive conclusions or recommendations based on rules and facts. The choice of approach depends on the problem domain, the available data, and the desired outcome.

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