A logistics company hires a large number of truck drivers. Each of the truck drivers contributes to

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Question:

A logistics company hires a large number of truck drivers. Each of the truck drivers contributes to the revenue of the company by 30, 000 +e (MXN$ monthly), where e is the effort of the driver that is not contractable - it might reflect how much the driver tries to do the deliveries fast and while saving gasoline, for example. Although the effort is usually not observed by the employer, the manager receives occasional signals about it.

As a result, depending on a driver's wage w (s)he chooses effort e(w) = max {0, 20, 000 log(w/10, 000)}.

(a) What is the profit-maximizing wage the logistic company should offer if number of drivers is fixed? Illustrate graphically

(b) What is the cost-minimizing wage and the number of workers N (regard N as a continuous variable) to have revenue R = 1, 000, 000? Characterize the solution implicitly as a root of an equation; to find solve the equation you will perhaps need to use numerical methods (e.g. use Matlab or www.wolframalpha.com). Illustrate graphically.

(I am having this much info only, as I have posted the same question/data that the professor has given to us.)