The President of a Consulting Firm Wants to Minimize the Total

Essay

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:
$$\begin{array}{l}\text { Project Hours }\\\begin{array} { | l | l | l | l | l | } \hline \text { Consultant } & \text { A } & \text { B } & \text { C } & \text { D } \\\hline \text { Charlie } & 13 & 16 & 11 & 18 \\\hline \text { Gerald } & 13 & 15 & 10 & 12 \\\hline \text { Johnny } & 15 & 11 & 20 & 15 \\\hline \text { Rick } & 17 & 17 & 12 & 22 \\\hline\end{array}\end{array}$$
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?