John's summer job is selling food concessions at the baseball stadium at home games. The director of concessions has offered John his choice of two jobs. First, he can work in the concession center under the seats for $65 per night or he can "hawk" soft drinks in the stands and be paid a percent of his sales. He has learned from other "hawkers" that your sales at the games is a function of the temperature at the start of the game. Since all of the games are night games and the stadium is always sold out at every game, temperature is the only variable of consideration. He has also learned that when it is very hot, his sales will earn him around $100; when it is just hot, he will earn $60; and when it is mild, he will earn $35 dollars. In checking with the Weather Bureau, he knows that during the sea son the probability of very hot is 30%, hot is 50% and mild is 20%. Which choice of jobs will maximize his earning potential over the summer?
Fixed earning that John would get by working in the concession center under the seats =$65
Earning through hawking of soft drinks has probability, which is a function of match-time temperature.
Probability of temperature remaining very hot`=30/(30+50+20)=3/10` and bearing earnings of $100
Probability of temperature remaining hot `= 50/(30+50+20)=1/2` and bearing earnings of $60
Probability of temperature remaining mild `= 20/(30+50+20)=1/5 ` and bearing earnings of $35.
Expected earnings by hawking in the soft drink stand
`= 100*(3/10)+60*(1/2)+35*(1/5) `
This is greater than what he would earn by working in the concession center.
Thus, soft drink sales through hawking will fetch John slightly more income.