Maxwell Professional Coaching $($MPC$)$ offers three coaching services for individuals at different career stages. Its prices and costs follow:

$$Price per UnitVariable Cost per UnitUnits Sold per YearEntry$ $240$$ $1402,200$Management$940540800$Executive$4,8003,020200$

Variable costs include the labor costs of the coaches who work as contract employees. Fixed costs of $$700,000$ per year include marketing, information technology, and other costs of administration. A basic $$unit$$ is a scheduled block of coaching and feedback sessions. The number of sessions in a block, the length of the sessions, and the experience of the coach vary across the services. The Entry service is designed for someone about to enter the job market, often about to leave college or be discharged from the military. The Management service is designed for those with some work experience who are about to take on managerial and supervisory duties. The Executive service is designed for those about to enter the top level of management at their organization.

Maxwell Professional Coaching is subject to a $23$ percent tax rate.

Required:

a$.$ Given this information, how much will MPC earn each year after taxes?

b$.$ Assuming the given sales mix is the same at the break$-$even point, at what sales revenue does MPC break even?

c$.$ At what sales revenue will MPC earn $$277,200$ per year after taxes assuming the given sales mix?

d$-1.$ MPC is considering becoming more specialized in Management and Executive services, or as the marketing manager puts it$,$ "our best clients." The marketing group has put together a plan that would result in the following changes. The number of Management clients would increase to $1,000$ per year and the number of Executive clients would increase to $400$ per year. At the same time, the number of Entry clients would drop to $600$ per year. After additional study, the MPC believes this would require an increase in fixed costs to $$950,000$ per year $($up from the $$700,000$ in fixed costs above$).$ Calculate the after$-$tax earnings.

d$-2.$ Considering this new information and if MPC$\text{'}$s managers seek to maximize the company$$s after$-$tax earnings, would this change be a good idea?