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 budget. Kramer estimates that the labor hours required for the next four quarters are $6,500,12,000,20,000,$ ?and $10,000,$ ?respectively. Each of the $11$ ?workers on the workforce 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

$ $3,700$

$,$ ?and the cost of laying off a worker is

$ $1,900$

$.$ ?Subcontracting is not permitted. $($ Hint: When calculating the number of workers, make sure to round up to the next whole number before proceeding with any further calculations. $)$ ?a $.$ ?Find a level workforce 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? $\backslash$ $ $.($ Enter your response as an integer. $)$ ?How many undertime hours does it call for? hours. $($ Enter your response as an integer. $)$ ?b $.$ ?Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this plan? $\backslash$ $ $($ Enter your response as an integer. $)$ ?c $.$ ?Consider the following proposed plan, for a different demand schedule, that combines the strategy of hiring, layoffs, and utilizing overtime. Payroll costs are

$ $6,000$

in wages per worker for regular time worked, with an overtime pay rate of

$ $18$

for each overtime hour. The cost of hiring a worker is

$ $3,700$

$,$ ?and the cost of laying off a worker is

$ $1,900$

$.$ ?The total cost for this plan would be

$

$.($ Enter your response as an integer. $)$