Westphalia Corporation produces audio equipment for home, office, and vehicles. The production manager $($PM$)$ and marketing manager $($MM$)$ are both are paid a flat salary and are eligible for a bonus. The bonus is equal to $2$ percent of company profit that is in excess of a specified target profit. $($All profit numbers exclude any bonus.$)$ The maximum bonus is $10$ percent of base salary. The PM$\text{'}$s base salary is $$200,000,$ and the MM$\text{'}$s is $$250,000.$

The target profit for this year is $$8$ million. The production manager has been approached by an engineering consulting firm that is willing to license to Westphalia a new manufacturing technique that would increase annual profit by $15$ percent, after deducting the licensing fee. The PM is unsure whether to employ the new technique this year, wait, or not employ it at all. Using the new technique will not affect the target.

Required:

a$.$ Suppose that profit without using the technique this year will be $$8$ million. By how much will the PM$\text{'}$s bonus change if the new technique is adopted? By how much will the MM$\text{'}$s bonus change if the PM decides to adopt the new technique?

b$.$ Suppose that profit without using the technique this year will be $$9$ million. By how much will the PM$\text{'}$s bonus change if the new technique is adopted? By how much will the MM$\text{'}$s bonus change if the PM decides to adopt the new technique?

c$.$ Suppose that profit without using the technique this year will be $$7$ million. By how much will the PM$\text{'}$s bonus change if the new technique is adopted? By how much will the MM$\text{'}$s bonus change if the PM decides to adopt the new technique?