Linear Programming
The director of passenger services for Ace Air Lines was trying to decide how many new flight attendants to hire and train over the next six months. The requirements in number of flight attendant flight hours needed were: Month Hours Needed January 8,000 February 7,000 March 8,000 April 10,000 May 9,000 June 12,000 The problem was complicated by two factors. It took one month to train flight attendants before they could be used on regular flights. Hence, hiring had to be done a month before the needs arose. Secondly, training of new flight attendants required the time of already trained attendants. It took approximately 100 hours of regular attendant time for each trainee during the month training period. In other words, the number of hours available for flight service by regular attendants was cut by 100 hours for each trainee. The director of passenger services was worried about January, because there were 60 attendants available. Company rules required that an attendant could not work more than 150 hours in any month. This meant that the director had a maximum of 9,000 hours available for January, 1,000 in excess of needs. (Attendants were not laid off in such cases; each merely worked fewer hours). Company records showed that 10 percent of the attendants quit their jobs each month for various reasons. The cost to Ace Air Lines for a regular flight attendant was $1,500 per month for salary and fringe benefits, regardless of how many hours worked (of course, one could not work more than 150 hours). The cost of a trainee was $700 per month for salary and fringe benefits. Formulate the above as a linear programming problem designed to solve the problem of the director of passenger services at minimum cost.
Answers
Step-by-step explanation:
Linear Programming
The director of passenger services for Ace Air Lines was trying to decide how many new flight attendants to hire and train over the next six months. The requirements in number of flight attendant flight hours needed were: Month Hours Needed January 8,000 February 7,000 March 8,000 April 10,000 May 9,000 June 12,000 The problem was complicated by two factors. It took one month to train flight attendants before they could be used on regular flights. Hence, hiring had to be done a month before the needs arose. Secondly, training of new flight attendants required the time of already trained attendants. It took approximately 100 hours of regular attendant time for each trainee during the month training period. In other words, the number of hours available for flight service by regular attendants was cut by 100 hours for each trainee. The director of passenger services was worried about January, because there were 60 attendants available. Company rules required that an attendant could not work more than 150 hours in any month. This meant that the director had a maximum of 9,000 hours available for January, 1,000 in excess of needs. (Attendants were not laid off in such cases; each merely worked fewer hours). Company records showed that 10 percent of the attendants quit their jobs each month for various reasons. The cost to Ace Air Lines for a regular flight attendant was $1,500 per month for salary and fringe benefits, regardless of how many hours worked (of course, one could not work more than 150 hours). The cost of a trainee was $700 per month for salary and fringe benefits. Formulate the above as a linear programming problem designed to solve the problem of the director of passenger services at minimum cost.