Summary of case study
George is a project manager who has a side hobbie of creating t-shirts for concerts, sporting events and other kind of events as well. For the shirts he sells them for a fixed price of $8.33 (as you will see as the fixed cost in the equations below) to each of his vendors who then goes to the events and sells them outside the actual events, for that he does not have actual rights to sell his merchandise inside the events. Below will be a detailed analysis of all 27 possible decisions that were/would be possible to choose from. Remember, George can only buy in bundles of 2,500 shirts; he bases his shirt ordering off of 10% of the total concert attendance, and has a good knowledge that the 20,000 standing tickets will be purchased fast, therefore he must guess whether there will be 80,000, 50,000 and 20,000 actual seats to be purchased. The other situation that happens (which will be shown in the equation’s) is that if the shirt count he wants/thinks he can sell at the concert are not able to be sold, those extra shirts are sold at a discounted price of $1.50, which as you can see is way lower price, however he is still selling them. Now the three different situations will be discussed as to what all the different variables/number mean in equation.
Decision’s for 5,000 t-shirts
To start off the decision tree, the decision for the 5,000 total shirts will be discussed first, for that it is apart of the top of the decision tree. The first four decision terminal nodes all have final valuations of $23,900, the only part which will be discussed per equation is the percent chance of happening. More so, in this equation there is the 5,000 shirts ordered at $8.33 a piece, however, before you can get the profit you must subtract out the cost which is $17,500. Lastly the percent chance of this happening per the estimated attendance is 60%. Again, with these percents, these represent George’s observance of the attendance at concerts when there was a certain amount of shirts purchased for a certain size range of people.
5,000*$8.33-$17,500=$23,900
This second equation looks exactly the same as the previous one, and it is the exact same in every sense, except for the hidden knowledge that this evaluation is based on a 30% chance that there will be at 5% off the attendance at the concert buy the shirts.
5,000*$8.33-$17,500=$23,900
The third equation in this bracket once again, looks exactly like the previous two, however, in this one, based on George’s assumption’s, there is a 10% chance that roughly 15% of the attendance will purchase a shirt.
5,000*$8.33-$17,500=$23,900
In this last equation of the first four that have the same evaluation of $23,900, in this situation, this is off the second major branch which is basing off a 50,000 grandstand in addition to the 20,000 standing tickets purchased. So in other words 70,000 tickets purchased. Going off this, with the same evaluation of $23,900, this is based off off a 50,000 grandstand in addition, and in this situation there is a 60% chance that 10% of the attending crowd should purchase a shirt.
5,000*$8.33-$17,500=$23,900
The rest of these evaluations based on the decision tree will for the most part have all different evaluations. In this next equation, the profit is $13,655, which is derived from the purchasing of 3,500 shirts at $8.33, as well as having 1,500 shirts being sold at $1.50. After doing that, you must subtract the added parts to the cost for the bundle of 5,000 shirts which is a cost of $17,500. This equation in also based off a 30% strong assumption by George that at least 5% of the attending audience will purchase a shirt from him,
3,500*$8.33+$1.50*1,500-$17,500=$13,655
In this next case we see there is a possibility of making a profit of $23,900. This is derived again from the possibility that all 5,000 shirts were purchased at the fixed rate of $8.33 a shirt, and then you must take out the cost for the bundle of shirts which is $17,750. There is a 1% chance of at least 15% of this crowd purchasing a shirt from him.
5,000*$8.33-$17,750=$23,900
This next case, there is a possibility of making a profit of $17,070. To get this, George’s vendors must sell 4,000 shirts at the fixed rate of $8.33, and then sell 1,000 shirts at the discounted price of $1.50. After this, the cost of the shirts which in this scenario is $17,750 must be taken off the profit. In this, there is a 60% chance that at least 10% of the audience will purchase a shirt from a vendor.
4,000*$8.33+$1.50*1,000-$17,750=$17,070
The next case has George making a profit of $3,410. This profit occurs by the vendors selling only 2,000 shirts at $8.33 and then 3,000 shirts at $1.50 a piece, then subtracting the cost for the bundle of shirts which is $17,750. As well, there is 30% chance of at least 5% of the attendees of the event to purchase a shirt.
2,000*$8.33+$1.50*3,000-$17,750=$3,410
For this last scenario of purchasing 5,000 shirts, George makes a profit of $23,900. In this case he sells all of the 5,000 shirts for a price of $8.33 and then must subtract the cost of the bundle which is $17,750. There is only a 1% chance of at least 15% of the crowd to purchase a shirt in this case. So to recap this decision, it is very unlikely for it to occur.
5,000*$8.33-$17,750=$23,900
Decision’s for 7,500 t-shirts
For this next series of 9 decisions, we will be looking at the decisions that reflect what a bundle of 7,500 shirts looks like with the different variations of possibilities. The first option is the possibility of making a profit of $37,225. To do this George must have all 7,500 shirts purchased at the price of $8.33, and then paying the cost off on them which is $25,250 for a bundle of 7,500 shirts. There is a 60% chance that at least 10% of the crowd of 100,000 will buy a shirt.
7,500*$8.33-$25,250=$37,225
In this next scenario, George has the ability to make a profit of $20,150. To do this he must sell 5,000 shirts at $8.33 and then sell the rest of the 2,500 shirts at $1.50, then factor in the cost of $25,250 for the bundle. There is a 30% chance that at least 5% of the crowd will purchase shirts in this case.
5,000*$8.33+$1.50*2,500-$25,250=$20,150
In this case, there is a possibility for a profit of $37,225. For this to happen, George would need all of the shirts, which would be 7,500 shirts to be sold at $8.33, and then apply the cost of $25,250 for the bundle. There is a 1% chance of at least 15% of the crowd to the buy shirts in this scenario.
7,500*$8.33-$25,250=$37,225
In this case George has the possibility of making a profit of $33,810. To do this he must sell 7,000 of his shirts at a price of $8.33 and then sell the remaining shirts for the reduced price of $1.50, and then take a way the cost for the bundle which is $22,250. There is a 60% chance that at least 10% of the crowd will attend and buy the shirts in this case.
7,000*$8.33+$1.50*500-$25,250=$33,810
In this case George has a chance to make a profit of $9,905. To do this though, he must sell 3,500 shirts at $8.33 a piece and then sell 4,000 of the shirts at a discounted price of $1.50 and then take into account the bundle cost of $25,250. There is a 30% chance that at least 5% of the crowd will attend and purchase a shirt in this case.
3,500*$8.33+$1.50*4,000-$25,250=$9,905
For this case George has the ability to make a profit of $27,225. To do so he must sell all 7,500 shirts at a cost of $8.33 and the pay the cost of $25,250 for the bundle of the shirts. In this there is a 1% chance of at least 15% of the crowd attending to purchase his shirts.
7,500*$8.33-$25,250=$37,225
For this case George has the ability to make a profit of $13,320. For him to have this happen, he must have 4,000 shirts sold at $8.33 and the other 3,500 shirts to be sold at the discounted price of $1.50 and the factor in the cost of $25,250 for the bundle of the shirts. There is a 60% chance that 10% of the crowd attending will purchase a shirt in this case, so a decent chance.
4,000*$8.33+$1.50*3,500-$25,250=$13,320
In this case George has a possibility of making a profit loss of -$340. For him to have the negative outcome happen, he must only sell 2,000 shirts at the $8.33 price and the rest of the 5,500 shirts at the lower price of $1.50 and then put in the cost of the bundle which is $25,250. There is a 30% chance that out the of the expected crowd at least 5% will purchase a shirt. Take into note, this is only 1 of the 2 possibilities that came out with a negative return.
2,000*$8.33+$1.50*5,500-$25,250=-$340
In this last case for the 7,500 bundle package, George has a chance to make a profit of $26,980. To do this he must sell 6,000 shirts at $8.33 and then the rest of the 1,500 shirts at $1.50, then factor in the cost of the bundle of the shirts which is $25,250. There is only a 1% chance that there will be 15% attendance of the crowd buying the shirts in this case.
6,000*$8.33+$1.50*1,500-$25,250=$26,980
Decision’s for 10,000 shirts
In this last set of decisions, George is dealing with a bundle of 10,000 orders, which is the highest amount in this case, with a cost of $32,125. In this first case, George has the ability to make a profit of $51,175. To do this he must sell 10,000 shirts at $8.33 and then pay the cost for the shirts at a price of $32,125. There is a 60% chance that 10% of the crowd attending will purchase a shirt made.
10,000*$8.33-$32,125=$51,175
In this next case, George has the ability of making a profit of $17,205. To do this he must sell 5,000 shirts at a cost of $8.33 and then the other 5,000 shirts at a cost of $1.50 a piece, as well as factor in the cost for the shirtss which is $32,150. There is a 30% chance that 5% of the attending crowd might buy the shirts.
5,000*$8.33+$1.50*5,000-$32,150=$17,025
In this case George has a chance to make a profit of $51,175. To do this great profit, he must sell 10,000 shirts at $8.33 and then factor in the cost for the shirts of $32,125. There is a 1% chance at there will be a 15% attendance of the crowd maybe buying the shirts.
10,000*$8.33-$32,125=$51,175
In this next case George has the ability to make a profit of $30,685. To do this George must sell 7,000 shirts at $8.33 a piece and then sell 3,000 shirts at the discounted $1.50 and then factor in the cost of $32,125. To get this there is a 60% chance that out of the crowd attending only 10% of the crowd will buy a shirt.
7,000*$8.33+$1.50*3,000-$32,125=$30,685
In this next case George has the ability to make a profit of $6,780. To do this George must sell 3,500 shirts at a price of $8.33 and the sell the remaining 6,500 shirts at a price of $1.50, and then factor in the cost of $32,125 for the shirts in the bundle. There is a 30% chance that 5% of the crowd that attended this event will purchase these shirts.
3,500*$8.33+$1.50*6,500-$32,125=$6,780
For this next scenario George has the chance to make a profit of $51,175. In order to do this he must sell all 10,000 shirts at the price of $8.33 and then factor in the cost for the bundle of shirts of $32,125. There is a 1% chance that 15% of the attending crowd will purchase the shirts from the vendor.
10,000*$8.33-$32,125=$51,175
In this scenario George has the chance to make a profit of $10,195. To do this he must sell 4,000 shirts at a price of $8.33 and the sell the other 6,000 shirts at the lower price of $1.50 and then factor the cost of $32,125 for the bundle of the shirts in. There is a 60% chance that 10% of the attending crowd will purchase a shirt from a vendor.
4,000*$8.33+$1.50*6,000-$32,125=$10,195
In this second to last case George has the ability to make a profit of -$3,465. To make this loss of a sell he must sell 2,000 shirts at $8.33 and the rest of the 8,000 shirts at the discounted rate of $1.50 and then factor in the cost of $32,125 for the bundle of shirts. For this there is a 30% chance that 5% of the attending concert will purchase the shirts from the vendor.
2,000*$8.33+$1.50*8,000-$32,125=-$3,465
In the last scenario, decision 27, George has the ability to make a profit of $23,855. To do this he must sell 6,000 shirts at $8.33 and the rest of the 4,000 shirts at the price of $1.50 and then factor in the cost of the shirts at $32,125. For this there is a 1% chance that 15% of the crowd attending will purchase a shirt from George.
6,000*$8.33+$1.50*4,000-$32,125=$23,855