George’s T-Shirts

George Lassiter was a project engineer for a major defense contractor. He had an interesting side business of manufacturing and designing T-shirts for rock concerts, sporting events, and fund-raising events. George sold the shirts to his regular crew of vendors for $100 per dozen, and these vendors sold the public for $10 per shirt. He wanted to sell his shirts on a rock concert that was going to be held in two months.

He was sure that 20,000 tickets for the standing area around the stage would be bought by devoted fans, but he was not sure of the number of people who will attend the concert, and the percentage of the attendees who will buy the shirts. George thought in terms of three possibilities specifically 80,000, 50,000 and 20,000 grand seats which he assumed to be high, medium and low respectively. The probability of 50,000 was as likely as either of the two possibilities combined. And 80,000 and 20,000 were about equally likely, or 80,000 was more likely than 20,000.

He also thought regarding his designs and quality of the shirts, his sales could be ten percent (about 6 times out of 10), five percent, or fifteen (1 time out of 10) percent of the attendance. George requested a cost estimate of shirts supply which is presented in the below table: Order Size Cost 10,000 $32,125 7,500 $25,250 5,000 $17,750 1. Standing Area Attendance 20,000

2. Sale Price to George from Concert Sales: $100 per Dozen or $8. 33 per T-shirt 3. Sale Price of leftover T-shirts to discount clothing chain $1. 50 Per T-shirt George’s Predictions Item/Option Qty Probability Grandstand Attendance-High 80,000 0. 3 Grandstand attendance-Medium 50,000 0. 5 Grandstand Attendance-Low 20,000 0. 2 Percent of Concert-goers to buy Shirt-High 15% 0. 1

Percent of Concert-goers to buy Shirt-Medium 10% 0. 6 Percent of Concert-goers to buy Shirt-Low 5% 0. 3 Objectives: 1. To find out how many people will attend the concert? 2. To find out how many people will buy T-shirts? 3. To calculate the financial outcomes of these three scenarios. 4. To maximize the profit. Decision Problem: How many shirts to order for the upcoming rock concert? Alternatives: The possible alternatives are 10,000, 7,500 and 5,000 shirts.

The decision will affect the costs and revenues generated from the sale of the number of shirts. The revenue will be affected by the sale price and sales volume. The sales volume is in turn affected by the number of attendees at the concert. Finally, the profit is a consequence of costs and revenues. When the order is 10,000 Attendance High (100000) Medium (70000) Low (40000) Percentage 10 15 5 10 15 5 10 15 5 Probability 0. 6 0. 1 0. 3 0. 6 0. 1 0. 3 0. 6 0. 1 0. 3 10000 15000 5000 7000 105000 3500 4000 6000 2000 Price per unit (8. 33) 83300 83300 41650 58310 83300 29155 33320 49980 16660

Price per unit for excess product(1. 5) 0 0 7500 4500 750 9750 9000 6000 12000 Cost 32125 32125 32125 32125 32125 32125 32125 32125 32125 Profit 51175 51175 17025 30685 51925 6780 10195 23855 -3465 When the order is 7500 Attendance High (100000) Medium (70000) Low (40000) Percentage 10 15 5 10 15 5 10 15 5 Probability 0. 6 0. 1 0. 3 0. 6 0. 1 0. 3 0. 6 0. 1 0. 3 10000 15000 5000 7000 105000 3500 4000 6000 2000 Price per unit (8. 33) 62475 62475 41650 58310 62475 29155 33320 49980 16660 Price per unit for excess product(1. 5) 0 0 3750 750 0 6000 5250 2250 8250 Cost 25250 25250 25250 25250

25250 25250 25250 25250 25250 Profit 37225 37225 20150 33810 37225 9905 13320 26980 -340 When the order is 5000 Attendance High (100000) Medium (70000) Low (40000) Percentage 10 15 5 10 15 5 10 15 5 Probability 0. 6 0. 1 0. 3 0. 6 0. 1 0. 3 0. 6 0. 1 0. 3 10000 15000 5000 7000 105000 3500 4000 6000 2000 Price per unit (8. 33) 41650 41650 41650 41650 41650 29155 33320 41650 16660 Price per unit for excess product(1. 5) 0 0 0 0 0 2250 1500 0 4500 Cost 17750 17750 17750 17750 17750 17750 17750 17750 17750 Profit 23900 23900 23900 23900 23900 13655 17070 23900 3410 Decision Tree : Conclusion