A local semiconductor firm, Superchip, is planning its workforce and production levels over next year. The firm makes a variety of microprocessors and uses sales dollars as its aggregate production measure. Based on orders received and sales forecasts provided by the marketing department, the estimate of dollar sales $($in $$10,000)$ for the next year by month is as follows: Month January February March April May June July August September October November December Production Days $221621192320241219222016$ Predicted Demand $340380220100490625375310175145120165$ Inventory holding cost is $$0\mathrm{.}25$ per dollar per year. It is anticipated that there will be $675$ workers on the payroll at the end of current year and inventories will amount to $$120,000.$ The firm would like to have at least $$100,000$ of inventory at the end of Dec. next year. It is estimated that each worker accounts for an average of $$60,000$ of production per year $($assume that one year consists of $250$ working days$).$ The cost of hiring a new worker is $$200,$ and the cost of laying off a worker is $$400.($a$)$ Determine the minimum constant workforce that will meet the predicted demand for the coming year, and evaluate the cost of this plan.