The president of a consulting firm wants to minimize the total number of hours it will take to complete four projects for a new client. Accordingly, she has estimated the time it should take for each of her top consultants—Charlie, Gerald, Johnny, and Rick—to complete any of the four projects, as follows:
![](data:image/png;base64, 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)
a. In how many different ways can she assign these consultants to these projects?
b. What is the total number of hours required by the following arbitrary assignment?
Charlie→B; Gerald→A; Johnny→D; Rick→C
c. What is the optimal assignment of consultants to projects? (Use the assignment method;
SHOW YOUR WORK!)
d. For the optimal schedule, what is the total number of hours it will take these consultants to complete these projects?
e. What is the significance, if any, of the fact that Gerald is the best performer at all four projects?