$1.$ Streets in Bellevue are maintained by Public Works Division; "Street Maintenance." Public Works administrators are planning the workforce of this division for next year. Labor hour requirements for the next year are $8,000,14,000,29,000,$ and $18,000,$ for quarters $1$ to $4$ respectively. Each of the current $15$ workers in the workforce can contribute $500$ hours per quarter. Overtime is limited to $20$ percent of the regular$-$time capacity in any quarter. Subcontracting is not permitted. Payroll costs are $$7,000$ in wages per worker for regular time worked up to $500$ hours, with an overtime pay rate of $$21$ for each overtime hour. Although unused overtime capacity has no cost$,$ unused regular time is paid at $$14$ per hour. The cost of hiring a worker is $$3,500,$ and the cost of laying off a worker is $$2,800.$

a$.$ Find a level workforce plan that uses overtime and the minimum amount of undertime $($idle time for workers$)$ possible. Overtime can be used to its limits $(20\%).$ What is the total cost of this plan?

b$.$ Plan for a chase strategy with variable workforce levels adjusted each quarter. What is the total cost of this plan?

c$.$ Propose a mix strategy. Compare your plan to plans $$a$$ and $$b$$ and show the differences. Is your plan better than plan $$a$$ or $$b$?$ Why or why not?

Please provide for each plan and each quater the following: workforce level, undertime hours, overtime hours, utilized time$-$hours, hires and layoffs