Question 2 Jack Makoena has been asked to organise the taxi service operating between Mamasweto and Durber- ley. He has already done a study to determine the needs of the commuters and plans to schedule the taxis so that the following numbers of taxis will be available during the different times of the day: Time of day 00:00 04:00 08:00 12:00 16:00 - - Number of taxis required 04:00 25 08:00 60 12:00 35 16:00 50 20:00 24:00 55 55 20:00 15 To meet this demand, Jack will contract a number of taxi drivers. Each one will work a shift of eight consecutive hours per day. There will be six different shifts, the first one starting at 0:00 and running until 8:00, the second one from 4:00 to 12:00, the third from 8:00 to 16:00, and so forth. Each taxi driver will be restricted to working in a specified time slot. If too many drivers are contracted, it may happen that the demand in a time slot is exceeded by far and the drivers will not be able to fill up their taxis to capacity. Thus, for the plan to work, the total number of taxi drivers should be kept to a minimum. 2.1 Formulate an LP model to determine how many taxi drivers to schedule in each eight-hour shift so that the demand for each four-hour time slot will be met and the total number of taxi drivers required will be a minimum. 2.2 Solve the model using SOLVER. Show that the demand in each period will be met by this solution. 2.3 Comment on the existence of alternative solutions.