Lassiter Shirts Case Summary

Mr. Lassiter has quite a dilemma on his hangs trying to figure out the correct number of shirts to buy to sell at an upcoming event. He buys the shirts in bulk and sells them at the price of $100 for a dozen, or $8.33 a piece, to vendors whom turn around and sell them for $10 apiece to event attendees. The only known number is 20,000 tickets being sold in the standing area. The number of tickets sold in the grandstands he thought would be the following possibilities: 80,000 tickets with a .26 probability, 50,000 tickets with a .50 probability, and 20,000 tickets with a .24 probability. The other unknown number was the percentage of attendees who would buy a shirt which hold the following probabilities: 15% at a .10 probability, 10% at
a .60 probability, and 5% at a .30 probability.
Estimated Value The grandstand ticket sales are a good place to start when determining estimated values. The weighted average calculation was used to determine the estimated value of grandstand ticket sales at 50,600 tickets. The calculation looks like this: (80,000 x .26) + (50,000 x .50) + (20,000 x .24) = 50,600 Next the percentage of ticket sales that will purchase a shirt is determined. This calculation also used the weighted average method and came in at 9%. The calculation looks like this: (.15 x .10) + (.10 x .60) + (.05 x .30) = .09 There are 20,000 guaranteed tickets and using the 9% estimated value of percentage of ticket sales that will bring shirt sales comes out to 1,800 shirts being sold.
Additionally 9% of the estimated value of tickets being sold, 50,600, is 4,554 in shirt sales. This brings a total of 6,354 in shirt sales for Mr. Lassiter. This number falls right in between the 5,000 and 7,500 order sizes that Mr. Lassiter can order shirts from his supplier in. On one hand he can pretty much be guaranteed that he will sell all 5,000 and make $23,900 in profit if he chooses to buy that amount; (4.78x5000=23900). He could potentially lose sales of 1,354 shirts totaling about $6,716 in pure profit; (25250/7500=3.37; 8.33-3.37=4.96 *which is the 7500 amount of per shirt profit;
4.96x1354=6715.84).
On the other hand he could potentially have an overage of 1,146 shirts if he buys 7,500; (7500-6354=1146).
Which Mr. Lassiter could sell to the discount clothing chain for $1,719, (1146*1.5=1719). If he buys 7500 for $25,250 or $3.37 a shirt and sells them all he will make $38,850; (4.96*7500=35850). He may still have the 1,146 left over shirts since the prediction is only to sell 6,354 shirts which may cost him $3,862; (3.37x1146=3862.02), but would make $1,719 back by selling them to the discount clothing chain putting his losses at only $2,139; (3859.0-1719=2139.2). This would also bring his profit down to $33,711; (35850-2143=33710.8). So, his loss is only 6% of his profit;
(2139/25850=.059).
Obviously if Mr. Lassiter chose to buy 10,000 shirts he would lose even more profit, but he would also bring in more profit even after the loss. He could purchase 10,000 shirts for $32,125 or $3.21 a shirt and make $5.12 a shirt; (8.33-3.21=5.12). He would make $51,175 in profit if he sold all 10,000; (5.12x10000=51175). Since he may only sell 6354 he would take a loss on 3,646 shirts coming out to $6,244; (3.21x3646=11712.78, 1.5x3646=5449, 11712.78-5469=6243.78). So, $51,175 - $6,244 = $44,931 in profit. This is only a loss of 12% of profit; 6244/51175=.12).
Conclusion
Basically Mr. Lassiter could buy either number of shirts from the supplier and make money it all depends on how much risk he is willing to take. He could buy 5,000 shirts and be pretty much guaranteed to sell all of them, but this also gives the lowest amount of profit. He could buy 7,500 shirts and possibly have a little left over if any and lose a little profit if all the shirts are not sold. Or he could buy 10,000 shirts and make the most profit even with a potential bigger loss than buying 7,500 shirts. I think that despite potentially not selling all of the shirts the greater profit per shirt when buying 10,000 proves to be the best way to go. The number of shirts bought should definitely cover all of the shirts he may sell and will more than cover a loss should he not sell all of the shirts. I think that the estimated value numbers are conservative numbers and there is a good potential for Mr. Lassiter to see greater ticket sales than being predicted which will bring greater shirt sales and a smaller loss.