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:
Assume there must be one-to-one matching between consultants and projects. What is the optimal assignment of consultants to projects?
A) Charlie to A; Betty to B; Johnny to C; Rick to D
B) Charlie to D; Betty to C; Johnny to B; Rick to A
C) Charlie to C; Betty to A; Johnny to D; Rick to B
D) Charlie to D; Betty to B; Johnny to C; Rick to A
E) Charlie to D; Betty to A; Johnny to C; Rick to B

Question

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: 
Assume there must be one-to-one matching between consultants and projects. What is the optimal assignment of consultants to projects?
A) Charlie to A; Betty to B; Johnny to C; Rick to D 
B) Charlie to D; Betty to C; Johnny to B; Rick to A 
C) Charlie to C; Betty to A; Johnny to D; Rick to B 
D) Charlie to D; Betty to B; Johnny to C; Rick to A 
E) Charlie to D; Betty to A; Johnny to C; Rick to B

Quizplus · Accepted Answer

To minimize the total number of hours, we should assign the consultant with the lowest estimated time to the project with the highest estimated time. Based on this, we can make the following optimal assignments:
- Charlie (5 hours) to project D (15 hours)
- Betty (6 hours) to project A (17 hours)
- Johnny (7 hours) to project C (19 hours)
- Rick (8 hours) to project B (21 hours)
This results in a total of 5+6+7+8 = 26 hours, which is the minimum total number of hours. Option E matches this assignment.

The President of a Consulting Firm Wants to Minimize the Total