One of Charlies earliest business ventures in the trading card business involved organizing local signing events for popular pro athletes. In the past he has hosted signing events by many big names in sports, including baseball players like Yogi Berra, Ted Williams, and Hank Aaron; he even hosted prizefighter Joe Frazier. Some of the signings made a good return, while others did not cover the costs involved in hosting the signing.

Charlie and The 7th Inning try to host at least one autograph session with a major sports figure each year. This year, he wants to bring Derek Jeter of the New York Yankees to Memphis for an autograph session. The going rate to bring a player of Dereks stature to a signing is $40,000 plus travel costs. For this fee, the athlete will spend around 46 hours at The 7th Inning and sign 1,000 items including photographs, baseballs, and reproduction jerseys. There is a bit of a hitch: the athlete usually specifies the maximum number of each item that he will sign. In this case, Derek will agree to sign up to 650 photos, 400 baseballs, and 100 jerseys. Charlie wants Joe and Sharese to help him figure out how many of each item they should have Derek sign in order to make the greatest potential profit overall and how much net profit they can make on the signing over costs, if they sell all of the items.

Item	Cost of item(per unit)	Cost of item including autograph cost	Recommended markup	Retail price after markup
8*10 Photographs	4	44	25%	55
Baseball	10	50	40%	70
Jersey	55	95	85%	176

	Number of items	Cost	Gross Profit	Net Profit
Photographs	500	22000	5500	5500
Baseball	400	20000	8000	8000
Jersey	100	9500	8100	8100
Travel cost	-	1000	-	-1000
Total	1000	52500	21600	20600

Working Notes-:

Cost of signing and travel expenses for each item=40000/1000 = 40 per items

Selling price of each item;

Photographs= (44*25%)+44

=55

Baseball = (50*40%)+50

= 70

Jersey= (95*85%)+95

= 176

Limitng factor analysis;

As the number of items is limited to 1000 we need to decide the number of each items to be produced. There a limitng factor analysis should be done.

	Photographs	Baseball	Jersey
Contribution per unit( Sales- direct cost)	11	20	81
Rank	3rd	2nd	1st

The product with highest contribution should signed most. So the number each items to be signed are as follows;

Item	Number of item
Jersey	100
Baseball	400
Photograph(b/f)	500
Total	1000

Total revenue of each item are;

Photographs= 500*55 = 27500

Baseball = 400*70= 28000

Jersey = 100*176 = 17600

• How would you factor in the $40,000 is costs to bring in a player like Derek?