The President of a Consulting Firm Wants to Minimize the Total

question 61

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

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Definitions:

Compounded Quarterly

The process by which interest is calculated and added to the principal sum of a loan or deposit four times a year.

Fifty-Fifty Sale

A promotional pricing strategy where items are offered for sale at a discount presumed to be 50% off their original price.

Conditional Sale Contracts

A conditional sale contract is a financing arrangement where the buyer gains possession and use of an asset, but title and ownership remain with the seller until the full purchase price is paid.

Compounded Quarterly

The process where interest is added to the principal sum of a deposit or loan every quarter, so that the added interest also earns interest from then on.