Reference no: EM131200008

The customer services department of a large retailer receives at least approximately 1200 emails from customers per day, all of which have to be replied to that day. The department employs two grades of staff: junior and senior. Both grades work for 8 hours per day, but junior staff can only process emails at a rate of 8 per hour compared to the senior rate of 10 per hour. Each member of staff requires a computer terminal and the department has a maximum of 25 terminals available. There is also a limited amount of desk space available (35m2 ). Each senior member of staff is expected to supervise junior staff, and hence senior staff are allocated more space (2m2 ) than junior staff (1m2 ). In order to ensure that proper supervision is always available, there must be at least 2 members of senior staff to every five junior members of staff. Taking into account all direct and indirect costs, the cost of employing a senior member of staff is $15 per hour, compared to $10 per hour for a junior member of staff. Show how this problem can be formulated as a linear program and derive the optimal solution to the problem, calculating exact values for all your variables and providing a practical interpretation of the solution.