a$.$ Based on this information, find the minimum constant workforce plan for Yeasty over the six months, and determine hiring, firing, and holding costs associated with that plan.

b$.$ Suppose that it takes one month to train a new worker. How will that affect your solution?

c$.$ Suppose that the maximum number of workers that the company can expect to be able to hire in one month is $10.$ How will that affect your solution to part $\backslash (($a$)\backslash )?$

d$.$ Formulate the problem levels as a linear program. $[$You may ignore the conditions in parts $($b$)$ and $($c$).]$

$\backslash ($ e $\backslash ).$ Solve the resulting linear program. Round the appropriate variables and determine the cost of your solution.

f$.$ Suppose Yeasty does not wish to fire any workers. What is the optimal plan subject to this constraint?