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, Betty, Johnny, and Rick-to complete any of the four projects, as follows:

Project (Hours)
Consultant A B C D
Charlie 13 16 11 13
Betty 11 15 14 18
Johnny 15 22 12 15
Rick 17 17 12 22

In how many different ways can she assign these consultants to these projects?

a. 4
b. 8
c. 24
d. 256
e. 16

What is the optimal assignment of consultants to projects?

a. Charlie to D; Betty to C; Johnny to B; Rick to A
b. Charlie to D; Betty to B; Johnny to C; Rick to A
c. Charlie to A; Betty to B; Johnny to C; Rick to D
d. Charlie to D; Betty to A; Johnny to C; Rick to B
e. Charlie to C; Betty to A; Johnny to D; Rick to B

For the optimal schedule, what is the total number of hours it will take these consultants to complete these projects?

a. 54 hours
b. 61 hours
c. 46 hours
d. 50 hours
e. 53 hours

She has four possible consultants for project A, after choosing one, she has three possible choices for project B, two for project C and is left with just one choice for project D. Therefore, the number of different ways she can assign these consultants is:

[tex]n=4*3*2*1\\n=24\ ways[/tex]

There are 24 ways.

Since this is a multiple choice question, the simplest way to solve it is to test the given alternatives to find out which one yields the least number of hours:

[tex]A = 13+14+22+17=66\\B=13+15+12+17=57\\C=13+15+12+22=62\\D=13+11+12+17=53\\E=11+11+15+17=54[/tex]

Therefore, alternative d. Charlie to D; Betty to A; Johnny to C; Rick to B is the optimal one.

As calculated above, it will take these consultants 53 hours to complete all projects.