A$.$ Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. $($Hint: Let x$,=$ number of full$-$time employees coming on duty at the beginning of hour i and y$,=$ numberof part$-$time employees coming on duty at the beginning of hour j$.)$If your answer is zero enter $"0"$ and if the constant is "I" it must be entered in the box.

B$.$ Solve the LP Relaxation of your model in part A$.$ Enter total number of full time and part time employees required

C$.$ Solve for the optimal schedule of tellers. Enter the total number of full$-$time and part$-$time employees required.If your answer is zero enter $"0".$Total Number of Full$-$Time Employees:Total Number of Part$-$Time Employees:

D$.$ After reviewing the solution to part $($c$),$ the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full$-$time employee is on duty at all times and that there is a staff of at least four fur employees. Revise your model to incorporate these additional requirements, and solve for the optimal solution. Enter the total number of full$-$time and part$-$time employees required and the total cost under the revised optimal solution.If required, round your answers to the nearest whole number. If your answer is zero enter $"0".$Total Number of Full$-$Time Employees:Total Number of Part$-$Time Employees:Total Cost: $