Question

[PLEASE ANSWER IN EXCEL TEMPLATE BELOW (A/B ON SEPARATE PAGES) AND SHOW FORMULAS/SOLVER INFO]

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:

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

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?

	English starts at 7	English starts at 10	English starts at 1	English starts at 4	Bilingual starts at 7	Bilingual starts at 10	Bilingual starts at 1	Bilingual starts at 4
Number assigned
Objective coeff
Constraints
7am-10am needs
10am-1pm needs
1pm-4pm needs
4pm-7pm needs
7pm-10pm needs
7am-10am English
10am-1pm English
1pm-4pm English
4pm-7pm English
7pm-10pm English
7am-10am Bilingual
10am-1pm Bilingual
1pm-4pm Bilingual
4pm-7pm Bilingual
7pm-10pm Bilingual
									LHS	Sign	RHS
	The optimal objective value is 24.

Answer 1

	7 am to 10 am	10 am to 1 pm	1 pm to 4 pm	4 pm to 7pm	7pm to 10 PM
Receptionist Needed	4	12	8	12	8
English receptionist ER	3	3+6	6	9	6
Bilingual receptionist BR	1	1+2	2	3	2

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
2. due to increase in demand we need to hire 8 more receptionist, 6 ER & 2 BR. They will work till 4pm. so now total receptionsists are 4+8 = 12
3. at 4 pm we all need 12 new receptionist. 9 ER & 3 BR. At 7 pm 4 among these wills stop working after 7 pm. total receptionist now are 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