Shift time Housekeepers 1 00:00-04:00 4 2 04:00-08:00 4 3 08:00-12:00 6 4 12:00-16:00 8 5 16:00-20:00 6 6 20:00-00:00 4 (a) Formulate a linear programming model from which the manager of the hotel can determine the minimum number of housekeepers to employ. [10 Marks] (b) Using the Two-phase simplex method, solve your linear programming model. [20 Marks] (c) The manager of the hotel decides to introduce a non-social hours rate of pay for any housekeeper who works during shift 1. The new rate is 150% of the normal rate and is paid for the whole eight-hour shift worked. The manager is also willing to increase the number of housekeepers employed in Shifts 1, 2 and 6. Formulate a linear pro- gramming model from which the manager of the hotel can determine the number of Security Officers to employ during each shift in order to minimise the total wage bill. [12 Marks] (2) The Grand Budapest Hotel employs housekeepers for twenty-four hours each day. The working day at the hotel is divided into 6 four-hour shifts starting at midnight. Each housekeeper works two consecutive shifts (that can be shift 6 followed by shift 1). The table below shows the minimum number of housekeepers needed for each shift 1