10- Suppose that the minimum number of security staff required at different hours are at the ith hour (i=1,2,,24) are outlined as follows: Hour beginning at 12am 1 2 3 4 5 6 7 8 9 10 11 12 Number of staff required 5 4 4 4 4 6 6 6 8 8 8 8 5 Hour beginning at 13 14 15 16 17 18 19 20 21 22 23 24 Number of staff required 5 5 5 8 8 8 9 10 10 10 10 8 Each staff must work in 6 consecutive hours. The salary per hour is $35. Determine how many staff should start working at the beginning of ith hour to minimize the total cost: a) Formulate the problem as a linear programming model. Write down the model and explain it. b) Solve the model in Excel and present the results and interpret them. c) If it is possible to ask a staff to stay extra 2 hours with salary of $45 per hour. Formulate the problem, write the mathematical model and explain it. d) Solve the model written in part c and explain the solution. (4+3+4+4=15 marks)