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Question 1186372: You are the manager of a restaurant and you want to optimize as well as maximize the working capacity of four of your employees. Baratie has 45 tables and each table seats 4 people. You have observed the average time (in minutes) each of your employees take to set a table as as the average time each take to fold the four napkins in the table which you have tabulated.
EMPLOYEE AVERAGE TIME TO SET A TABLE
Patty 5
Carne 7
Sanji 4
Luffy 3
EMPLOYEE AVERAGE TIME TO FOLD 4 NAPKINS
Patty 4
Carne 3
Sanji 2
Luffy 5
First Situation: In order for your restaurant to be ready for opening in the least amount of time, which two among your employees should you assign to fold the napkins? How about which two should be assigned with the setting of the tables?
Second Situation: If all your employees start working at the same time (which means that if an employee is done, he should help another employee), how quickly can all the tables be set? How about all the napkins be folded?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's an analysis of your employee assignments to optimize and maximize working capacity:
**First Situation: Minimizing Preparation Time**
* **Napkin Folding:** To minimize the total time spent folding napkins, assign the two fastest employees. Sanji (2 minutes/table) and Carne (3 minutes/table) should fold napkins.
* **Table Setting:** To minimize the total time spent setting tables, assign the two fastest employees. Luffy (3 minutes/table) and Sanji (4 minutes/table) should set tables.
**Second Situation: Parallel Work and Fastest Completion**
Here, we want to minimize the *longest* task completion time, as that determines when the *entire* task (either tables or napkins) is finished. We need to balance the workload.
* **Table Setting:**
* Luffy and Sanji are still your best bet for table setting.
* Combined setting time: (45 tables) / (1 table/3 min + 1 table/4 min) = 45 / (7/12) ≈ 77.14 minutes
* **Napkin Folding:**
* Sanji and Carne are still your best bet for napkin folding.
* Combined folding time: (45 tables) / (1 table/2 min + 1 table/3 min) = 45 / (5/6) ≈ 54 minutes
Since the table setting takes longer (approximately 77.14 minutes) all the tables will be set in approximately 77.14 minutes. The napkin folding will be done in 54 minutes, so all the napkins will be folded in approximately 54 minutes.
**Summary:**
* **First Situation:**
* Napkins: Sanji & Carne
* Tables: Luffy & Sanji
* **Second Situation:**
* Tables: Luffy & Sanji (approx. 77.14 minutes)
* Napkins: Sanji & Carne (approx. 54 minutes)
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