For the following question. Include your derivation steps and explanation in text. You will not be awarded points if you are missing the derivation steps and just write the answer, unlike the earlier assignment 1. Expect : Mid-term 2 exam. Appreciate your own words on the assignments, please avoid any copy-paste.

The Barberton Municipal Division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Cindy Kramer, road maintenance director, must submit a staffing plan for the next year based on a set schedule for repairs and on the city bud-get. Kramer estimates that the labor hours required for the next four quarters are 6,000, 12,000, 19,000, and 9,000, respectively. Each of the 11 workers on the work-force can contribute 500 hours per quarter. Payroll costs are $6,000 in wages per worker for regular time worked up to 500 hours, with an overtime pay rate of $18 for each overtime hour. Overtime is limited to 20 percent of the regular-time capacity in any quarter. Although unused overtime capacity has no cost, unused regular time is paid at $12 per hour. The cost of hiring a worker is $3,000, and the cost of laying off a worker is $2,000. Subcontracting is not permitted.

a. Find a level staffing plan that relies just on overtime and the minimum amount of undertime possible. Overtime can be used to its limits in any quarter. What is the total cost of the plan and how many undertime hours does it call for? [0.5 point]

b. Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this plan? [0.25 point]

c. Propose a plan of your own. Compare your plan with those in parts (a) and (b), and discuss its comparative merits. [0.25 point]

Please show step by step work