let xx$=16$

$($a$)$ Using level strategy, find the minimum constant workforce plan for the six months, and the total cost of the plan. Shortages are not permitted at any time. The plan should show the production and subcontracting levels, workforce levels, number hired, number fired, and ending inventory for each month. You may hire or fire workers only at the start of Jan, and no overtime production is allowed. Calculate the cost of this plan

$($b$)$ Determine the zero inventory $($chase$)$ plan that hires and fires workers each month to match demand as closely as possible, and the cost of that plan. No stockouts or overtime is allowed.

$(10$ points$)$

$($c$)$ Find an aggregate production plan that uses a constant workforce, and where backorders are allowed only in the months of January, February and March. You may hire or fire workers only at the start of Jan, and no overtime production is allowed. Calculate the cost of this plan. $(10$ points$)$

$($d$)$ Determine a constant workforce plan that uses only $30$ workers employed at the start of January. Use overtime hours to increase production levels when necessary to meet demand. What is the cost of this plan? $(10$ points$)$

$($F$)$ Formulate a mathematical model using Excel solver to generate the aggregate optimal production plan for the constant workforce strategy in part $($a$).$ The Excel sheet should be able to calculate the decision variables, as well as the total cost, which can be checked by comparing it to the results obtained in part $($a$).(20$ points$)$

$($E$)$ Formulate a mathematical model using Excel solver to generate the aggregate optimal production plan, allowing all options in all months. Compare the total cost of this aggregate production plan with the total costs of the strategies used in parts $($a$),($b$)$ and $($c$).(20$ points$)$

$($g$)$ By changing the values of cost parameters such hiring$/$firing$,$ inventory, variable production, and overtime, realize the potential trade$-$offs between decision variables and explain how the observed results will validate the model behavior mathematically.