Problem

An airline with operations in San Diego, California, must staff its ticket counters inside the airport. Ticket attendants work 6-hour shifts at the counter. There are two types of agents: those who speak English as a first language and those who are fully bilingual (English and Spanish). The requirements for the number of agents depend on the numbers of people expected to pass through the airline's ticket counters during various hours. The airline believes that the need for agents between the hours of 6 a.m. and 9 p.m. are as follows:

Agents begin work either at 6 a.m. , 9 a.m. , noon, or 3 p.m. The shifts are designated as shifts A, B, C, and D, respectively. It is the policy of the airline that at least half of the agents needed in any time period will speak English as the first language. Further, at least one-quarter of the agents needed in any time period should be fully bilingual.

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

(b) What is the optimal hiring plan from a cost perspective if English-speaking agents are paid $25 per hour and bilingual agents are paid $29 per hour? Does the total number of agents needed change from that computed in part (a)?