Question $1(25$ points$).$ A call center is open $7$ days per week from $8$:$00$am to $7$:$00$pm and uses hourly planning intervals. The minimum number of call center agents required in each hour of each day is shown in the table below. The call center will be staffed using full$-$time and part$-$time agents who each work five consecutive days per week. All seven possible patterns of five consecutive workdays are permissible. Each agent will begin their shift at the same time on each day of their work week. Full$-$time shifts span nine hours with a one$-$hour meal break after fourth hour $($i$.$e$.,4$ hours of work, a $1-$hour break, then $4$ more hours of work$).$ Part$-$time shifts span $5$ consecutive hours with no meal break. Full$-$time agents are paid $$720$ per week and part$-$agents are paid $$375$ per week. The call center would like to construct a weekly work schedule that will minimize the weekly staffing costs, while assuring that there are a sufficient number of agents present to meet the minimum requirements in each hour of each day of the week. Build an integer linear programming model in Excel to solve this problem. Then use the Excel Solver to obtain solutions for each of the following conditions: $(1)$ Using FT agents only, $(2)$ Using PT agents only, $(3)$ Using both FT and PT agents with a limit that no more than $20\%$ of the agents can be part$-$time employees, $(4)$ Using both FT and PT agents with a limit that no more than $30\%$ of the agents can be part$-$time employees, and $(5)$ Using both FT and PT agents with a limit that no more than $40\%$ of the agents can be part$-$time employees $.$

For each condition, your answer should provide the following information: $($i$)$ number of FT agents, $($ii$)$ number of PT agents, and $($iii$)$ total weekly staffing cost.

For the last condition only, your answer should provide: $($a$)$ a screenshot showing a portion of the FT schedule assignments, $($b$)$ a screenshot showing a portion of the PT schedule assignments, and $($c$)$ a screenshot of the Solver dialog box.

Comment on the $5$ solutions that you obtained. What would you recommend to the call center?$\backslash$table$[[,8-9am,9-10am,10-11a,11-12p,12-1pm,1-2pm,2-3pm,3-4pm,4-5pm,5-6pm,6-7pm$