La Quinta Inn is staffing its receptionists in its biggest hotel in San Antonio.

ID: 398338 • Letter: L

Question

La Quinta Inn is staffing its receptionists in its biggest hotel in San Antonio. Receptionists work 6-hour shifts at the hotel lobby. There are two types of receptionists: those who speak English as a first language and those who are fully bilingual (English and Spanish). The requirements for the number of receptionists depend on the customer arrivals during various hours. The Inn believes that the need for receptionists between the hours of 7 A.M. and 10 P.M. are as follows:

Receptionists begin work either at 7 A.M., 10 A.M., 1 P.M., or 4 P.M. At least half of the receptionists needed in any time period should speak English as the first language. Further, at least one-quarter of the receptionists needed in any time period should be fully bilingual.

A) How many and what type of receptionists should be hired for each shift to meet the language and staffing requirements, so that the total number of receptionists is minimized?

B) What is the optimal hiring plan from a cost perspective if English-speaking receptionists are paid $30 per hour and bilingual receptionists are paid $35 per hour?

7am to 10am 10am to 1pm 1pm to 4pm 4pm to 7pm 7pm to 10pm Receptionist Needed 4 12 8 12 8

Explanation / Answer

Conditions

Solution:

7am to 10am

10am to 1pm

1pm to 4pm

4pm to 7pm

7pm to 10pm

Receptionist Needed

English receptionist ER

3 + 6

Bilingual receptionist BR

1 + 2

Step 1: to keep the labor cost to its minimum we need to keep the BR at minimum requirement. Therefore, at 7 am we require 3 ER & 1 BR. They will work till 1 pm. Total receptionists = 4

Step 2: due to increase in demand we need to hire 8 more receptionists, 6 ER & 2 BR. And they will work till 4pm. Total receptionists now= 4 + 8 = 12

Step 3: at 4 pm, we need all 12 new receptionists, 9 ER & 3 BR. 4 among these will stop working after 7 pm. Total receptionists now= 12 + 12 = 24

So total no. of receptionists required are 24. ER = 3+6+9= 18, BR = 1+2+3= 6

Now, cost of ER for working 3 hours= 3*$30 = $90

Therefore, cost of ER receptions = 18*$90= $1720

Now, cost of BR for working 3 hours= 3*$35 = $105

Therefore, cost of BR receptions = 6*$105= $630