The Barberton Municipal division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Vijay$$ Gupta, road maintenance$$ director, must submit a staffing plan for the next year based on a set schedule for repairs and on the city budget. Gupta estimates that the labor hours required for the next four quarters are $7,000,12,500,19,000$and $10,000$ respectively. Each of the $11$ workers on the workforce can contribute $500$ hours per quarter. Payroll costs are $$6,000$ in wages per worker for regular time worked up to $500$hours$,$ with an overtime pay rate of $$17$ 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 $$12$ per hour. The cost of hiring a worker is $,$$$3,400$ and the cost of laying off a worker is $$1,200.$ Subcontracting is not permitted. $($Hint: When calculating the number of$$ 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$$ plan? $$$

How many undertime hours does it call$$ for?

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

Part $4$

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

$$

Part $5$

c$.$ Consider the following proposed$$ plan, for a different demand$$ schedule, that combines the strategy of$$ hiring, layoffs, and utilizing overtime. Payroll costs are in wages per worker for regular time$$ worked, with an overtime pay rate of for each overtime hour. The cost of hiring a worker is $,$ and the cost of laying off a worker is $.$

Quarter

Demand

$($hours$)$

Workforce

Hires

Layoffs

Overtime

$($hours$)$

$1$

$6,000$

$12$

$1$

$2$

$12,000$

$24$

$12$

$3$

$19,000$

$31$

$7$

$3,500$

$4$

$9,000$

$18$

$13$

Total

$85$

$20$

$13$

$3,500$

The total cost for this plan would be $$$