Mr$.$ Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion, Michigan. Based on orders received and forecasts of buying habits, it is estimated that the demand for the next four months is $850,1,260,510,$ and $980,$ expressed in thousands of cookies. During a $46-$day period when there were $120$ workers, the company produced $1\mathrm{.}7$ million cookies. Assume that the number of workdays over the four months are respectively $26,24,20,$ and $16.$ There are currently $100$ workers employed, and there is no starting inventory of cookies.

$a.$ What is the minimum constant workforce required to meet demand over the next four months?

$b.$ Assume that $c_{\text{I}}=10$ cents per cookie per month, $c_H=$$$100,$ and $c_F=$$$200.$ Evaluate the cost of the plan derived in part $($a$).$