George Is A Project Manager With A Side Hobby Of Creating

George Is A Project Manager Who Has A Side Hobbie Of Creating T Shirts

George is a project manager with a hobby of creating T-shirts for concerts, sporting events, and other occasions. He sells these shirts for a fixed price of $8.33 to vendors who sell them outside the events, as he does not have rights to sell inside. George must decide on the number of shirts to order, always in bundles of 2,500, based on an estimate of attendance, which he approximates as 10% of the concert's total attendance. He considers three possible total attendance scenarios: 80,000, 50,000, and 20,000 tickets. If sales are lower than expected, unsold shirts are sold at a discounted price of $1.50. The analysis evaluates 27 decision options involving different quantities of shirts—5,000, 7,500, and 10,000—each with multiple probabilistic outcomes, based on the percentage of the crowd purchasing shirts and the likelihood of certain attendance figures.

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In the context of entrepreneurial decision-making within the event merchandise market, George's strategic choices exemplify the complex interplay between demand forecasting, inventory management, and pricing strategies. His hobby of creating T-shirts for events encompasses a multitude of decision scenarios that must be evaluated through probabilistic analysis to maximize expected profit, considering uncertain attendance figures and consumer purchase behaviors.

At the core of George's decision-making process is the determination of order quantity—either 5,000, 7,500, or 10,000 shirts—each associated with specific costs and potential revenues. For each quantity, multiple avenues are examined, reflecting different sales mixes and price points contingent on consumer purchase probabilities. For instance, in the scenario of ordering 5,000 shirts, profit outcomes range from $3,410 to $23,900, depending on factors such as the percentage of attendees purchasing at full price versus the discounted price and the likelihood of those attendance levels materializing. These outcomes are calculated by multiplying the number of shirts sold at each price by that price, then subtracting the fixed costs associated with bundles, which vary based on the order size.

Specifically, the highest probability of success hinges on selling the entire stock at the full price of $8.33 per shirt, resulting in the maximum profit, with a marginal probability (1%) of achieving a significant 15% attendance, which would justify the full inventory sale. Conversely, in less favorable outcomes—such as lower attendance or reduced sales—unsold shirts are liquidated at the lower price point of $1.50, lowering overall profit but mitigating potential losses.

Similar analyses extend to larger order quantities, such as 7,500 shirts, where profit ranges are broader, from as low as $9,905 to as high as $37,225. Notably, the probabilities associated with these scenarios—e.g., a 60% chance of selling at least 10% of the shirts—inform the expected value computations necessary for informed decision-making. These calculations encapsulate the uncertainty inherent in demand estimation and highlight the importance of probabilistic modeling in entrepreneurial risk assessment.

Further, the assessment of 10,000 shirts demonstrates the escalating risk and reward dynamics. The highest expected profit remains at $51,175, realized under optimal conditions where all shirts are sold at $8.33, coupled with high attendance scenarios (15% or more). Conversely, lower probability, adverse situations—such as only 5% attendance—yield significantly reduced or negative profits, exemplified by a -$3,465 outcome when a substantial number of shirts are sold at discounted prices.

This comprehensive decision tree analysis underscores several key entrepreneurial principles. First, the importance of demand forecasting accuracy directly influences profitability. Second, inventory bundling strategies (ordered in multiples of 2,500 shirts) must balance order quantity against expected sales probabilities to optimize expected value. Third, dynamic pricing—selling excess inventory at discounted rates—serves as an essential risk mitigation measure in uncertain demand environments.

In conclusion, George's scenario provides an illustrative case of how probabilistic decision analysis can guide entrepreneurs in managing inventory, pricing, and risk under demand uncertainty. By quantifying potential outcomes and associated probabilities, he can make more informed choices about order sizes and sales strategies, ultimately enhancing his expected profitability. This approach aligns with core entrepreneurial competencies—risk assessment, demand estimation, and strategic resource allocation—integral to successful small business operations in dynamic markets.

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