Suppose the constant workforce plan determined in part $($a$)$ is going to be deployed, and each agency can work up to $8$ hours as regular production time each day $($assuming the $22,080$ units in the problem statement are produced by the $40$ workers working exactly $8$ hours each day during the quarter$).$ Assume that regular hourly rate XYZ pays to the staffing company is $$12$ per agency. Assume each agency can work overtime at $1\mathrm{.}5$ rate. The overtime cannot exceed $25\%$ of the regular production time. Also, XYZ needs to pay tax for the existing inventory at the end of each quarter. The quarterly tax for each item in inventory is $$2.$ Formulate an integer program to find minimum cost plan for the upcoming year.