1. A consulting firm must decide now whether to hire a youngengineer. The main purpose of this engineer would be to work on acontract that the firm hopes to win. This new contract will beginin 2 months and last for 4 months. If the firm hires the engineerand wins the contract, the firm will make a profit of $6000 on thenew contract (this figure allows for the cost of the new engineerduring the 4 months of the contract). During the new employee’sfirst 2 months (before the new contract begins), he can be assignedto various projects, reducing overtime costs for other employees by$1200 per month. The cost of employing this engineer (salary,taxes, and benefits) is $2,000 per month, so it is clear that thefirm will lose money on him for his first 2 months. If the firmhires the engineer but does not win the contract, it cannot firehim until he has completed 3 months of work. During the third monthhe will not really be needed, and the work he will do will be worthonly $400 to the firm. If the firm does not hire the engineer butwins the contract, it will be forced to hire somebody in a rush.There is only a 45% chance that it would be able to find anotheryoung qualified engineer on such notice for $2000/month, and if itis unable to find one it will have to pay $3,000/month for anexperienced engineer to work 4 months on the project.
a) The president of the firm feels the firm has a 60% chance ofwinning the contract. Should it hire the engineer now or wait untilit knows whether it won the contract?
b) What is the “indifference probability†of winning thecontract, i.e. the probability at which the firm is indifferentbetween hiring the engineer now and waiting until it knows whetherit won the contract?
2. On the first of the month, you must decide whether or not tobuy a monthly bus pass for $25. You usually drive to work, but yourcar must go in for service, and you will be forced to ride the bus.Over the phone, the mechanic estimated an 80% chance that the car’sproblem is major, requiring 10 working days of service. However, ifthe mechanic finds only a “minor†problem, you will be without thecar for only 5 working days. The bus fare is $3.00 per day. Shouldyou buy the bus pass? Base your decision on the expected cost ofriding the bus for the month.
