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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:

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

Required:
a. In how many different ways can she assign these consultants to these projects?
b. What is the optimal assignment of consultants to projects?
c. For the optimal schedule, what is the total number of hours it will take these consultants to complete these projects?

Sagot :

Answer and Explanation:

The computation is shown below

a. The different number of ways would be  

Since the number of consultants is 4 and the projects are also 4 so the Number of ways they can be assigned is 4!

= 4 × 3 × 2 ×1

= 24

b. Charlie to C; Betty to A; Johnny to D; Rick to B

In this case, we can see that in the chart that Charlie takes to complete C at the less time so Charlie will do C and according to this Betty will take minimum time for A likewise the others are picked up.

16. The total no of hours is  

Time taken by charlie = 11

Betty = 11

Johnny = 15  

Rick = 17

Total = 11 + 11 + 15 + 17

Total = 54

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