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Answer to Question #2769 in Statistics and Probability for winston

Question #2769
The waiting time in hours, W, of cars sent to a workshop is random with the following distribution f(w)=0.5e^-0.5w w>0. The profit, P, that the workshop makes is the following function of W:P=cN-8W where c is a constant and N is the number of cars waiting in the workshop. If there are 10 cars waiting, for what value of c will the expected profit be (i) positive (ii) More than $54.00?
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