Joe's Tavern

I borrowed a book from my Linear Programming professor to practice some network flow problems and I found this one that I thought you'd enjoy.

Joseph R. Smithey owns and runs a tavern on the "main drag" adjacent to the Big State University campus. For this reason, the majority of his clientele are university students. Joe has an understanding with the University Police Department. Since the officers have been around a little while, they know that college students have a tendency to be somewhat more rowdy than ordinary bar customers. However, the police require that Joe not let his customers get so drunk that they fall off their bar stools.

Joe has somewhat of a dilemma. His continued economic livelihood depends upon both happy customers and happy policemen. Here is a situation typical of most any night at the tavern.

Four thirsty customers from the Brazos Coop are sitting at the bar with 40 oz. of Jack Beem to divide between them. (Needless to say, none will be left when the evening is over.) Since Joe will be pouring, he largely controls the amount of Jack Beem that each customer will receive.

Being a good host, Joe knows each customer should receive at least 3 oz of the liquor. However, since customer 1 bought the bottle it is certain he will complain unless he receives at least 15 oz. Further, customer 3 has liver problems and should receive no more than 5 oz.

The probability that customer i will not fall off his stool after drinking xi ounces of Beem is

Pi=e^-Lixi, where L1=.01, L2=.05, L3=.10, and L4=01.

How many ounces of Beem should Joe give each customer in order to maximize the probability that all four customers stay on their stools?

There's a solution that I'll be happy to share with anyone who's interested.  Amazing how network flow can be used to solve so many different problems.

My friend and I had planned all week to go to the Alpha Psi Rodeo today, but we changed our mind this morning.  It is actually the Alpha Psi Roundup, tickets are $30 per person, and when my friend was at Kroger at 8 AM this morning, the lines at the checkout counters were longer than she'd ever seen them and each college student in line had a case of beer!  Probably not my kind of event.  I'll just be happy at the "show-de-os" where junior high and high school students in Poplarville perform.  We sold one of our Dexter bulls to the Poplarville arena and he's so low to the ground, none of the young cowboys can ride him successfully.

I've worked on Particle Swarm Optimization all day and I've reached optimality--hurray!  My programming skills and my experimental design skills are improving.