Statistics in Contemporary Business

Statistics in Contemporary Business
Executive Summary
George is aiming to maximize his profit from selling the shirts while at the same time minimizing his losses and expenses. To maximize his profit, he intends to order an amount of shirts that will all be sold at the concert. For every unsold shirt, he only recovers an amount of the initial amount spent buying it by disposing it at $1.50. To minimize his expenses, he has to order an amount of shirts that will be sold entirely while taking advantage of the volume discount offered.
Decision problem
First, George has to decide between the possibilities of High, Medium and Low sales of the grandstand seats to the concert as the 20000 standing area tickets are guaranteed to be sold. This choice will directly affect some shirts to order to meet the demand. Between the three order sizes that are multiples of 2500, George has to make the order size to meet the anticipated attendance and sales at the concert. The right order size will minimize losses in revenue through the disposal of leftovers at a lower price and take advantage of volume discounts.
The industry George’s company is operating in deals with goods with a short lifecycle, after which they lose their value. The shirts are only valuable for each event they are made for, after which their value falls and they can only be sold at a fraction of the price. Another product that can be considered similar is daily newspapers, which cannot be sold at the same price a day after. The company’s sales cannot be determined with certainty, and probabilities are used to estimate expected sales. Probabilities are used to predict the number of attendees to the events and the number of attendees likely to buy the shirts as well. Demand side probabilities are afterward used to estimate the volumes of the supply side to order.
Decision alternatives George has to make are between orders of 5000, 7500 and 10000 shirts. A larger order has a volume discount. He also has to decide on the percentage of people attending the concert interested in buying the shirts being 5%, 10% or 15% of the total attendance. Given his expectation of a medium attendance of 50000 grandstand seats and the guaranteed 20000 for the standing area, 10% of the total of 70000 gives a minimum of 7000 shirts. An order of 7500 shirts will cost $25250. Selling 7000 shirts to agents at $100 per dozen will generate a revenue of $58300 from 583 dozens. 504 remaining shirts are sold at $1.5 each bringing the total revenue to $59056. The profit is $33806, the difference between $59056 and $25250 ( Kuiper and Clippinger, 2012).
Compare this to his preferred order of 5000 shirts. They will cost $17750. Selling them to agents at $100 a dozen he will make $41600 from 416 dozens.8 surplus shirts sold at $1.50 each will generate $12. The total revenue is, therefore, $41612. Subtracting the cost of $17750 from this gives a profit of $23862. However, this order will not meet the expected demand of 7000 shirts, leaving a shortfall of 2000 shirts which means lost revenue for George.
Although the order of 5000 shirts is less risky and means that fewer shirts are sold for a cheaper price, it falls short of meeting the expected demand. I would recommend an order of 7500 shirts which yields higher profits, even with more shirts being sold for $1.50.George should, therefore, opt for the less conservative order of 7500 shirts that will give him better profits than 5000 shirts he intends to order.
Reference
Kuiper, S., &amp. Clippinger, D. (2012). Contemporary Business Reports. Cengage Learning.

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