What is capacity planning? Explain the decision theory. Solve the example below using the decision tree method.

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What is capacity planning? Explain the decision theory. Solve the example below using the decision tree method.
Example: A business has to choose one of two options, either to establish a factory with all functions in terms of the products it will produce, or to establish a pilot factory to expand it later. The decision depends on the future demand of the product to be produced. If the demand for the product increases, it will be more economical to set up the entire factory. On the other hand, if the expansion can be completed within two years, the option of establishing a small factory may also be considered.
Based on a simple market review, the probabilities of increase and decrease in demand over 10 years are estimated to be 75% and 25%, respectively. The cost of establishing the entire factory is 5 million dollars, and the cost of establishing a pilot factory is 1 million dollars. If the pilot factory were to be expanded in two years, the cost would be 4.2 million dollars.
The annual return estimates for each alternative are as follows. What size factory should be invested in.
• As a result of the establishment of the entire factory, the annual return of excess demand will be 1 million dollars (300,000 dollars for low demand),
• Pilot plant and low demand will bring in $200,000 per year,
• Pilot plant and excess demand will bring in $250,000 per year for ten years,
• Expansion of the pilot plant and in case of high demand, it will be $900,000 annually ($200,000 in case of low demand),
If the pilot plant is not expanded, there will be excess demand in the first two years, demand will fall in the following years, and the return for each of the remaining 8 years will be $200,000.