SaaSafras$$ business has been stable with some organic growth and some natural churn. Planterbox has identified you as a rising star within the org and you$$ve been hand picked to run the newly acquired business after the previous CEO of SaaSafras retired and sold their business. You$$re excited for the opportunity and your first project is to figure out how you can grow SaaSafras$$ revenue $($Planterbox decided they loved the name too much, even though they acquired the company they$$ll keep the SaaSafras name$).$ As part of the acquisition, you$$ve inherited $20$ great people who can do it all between sales, account management and support. Unfortunately, doing it all has come at a cost and productivity has been lower than if they had specialized in any of the individual roles $($and they are begging for specialization as well$).$ Going forward each person will only perform one core role at a time. While each person will only perform one role at a time they can switch to another role at the start of any month $-$ one person could cycle through every job without a loss in productivity. Your goal is to maximize SaaSafras$$ cumulative revenue over the next $24$ months. $($the sum of all revenue generated over $24$ months$).$Your responsibility is to determine where these $20$ people will work each month for the next $24$ months to maximize the cumulative revenue generated over the entire period.

The three roles are: $1.$ New Business Acquisition a$.$ These people are responsible for selling and getting new customers in the door $2.$ Account Management a$.$ These people help existing customers; they drive revenue growth from the customers they work with and improve retention $3.$ Support a$.$ These people solve customer problems; they improve retention for any active customer SaaSafras has some key metrics that won$$t change with the acquisition. The business currently has $1,000$ customers. SaaSafras acquires $25$ customers a month organically through great branding and customer referrals. Some customers turn to other, more specialized solutions and monthly churn is $10\%.$ There has been a standalone support org in addition to your swiss army knife team, and support$$s CSAT $($Customer Satisfaction$)$ has been steady at $70\%$ for several years. SaaSafras doesn$$t offer any discounts and every active customer pays a baseline fee of $$100$ a month for the core product.

Team specifics are below: People who work on New Business Acquisition acquire $5$ new customers a month. Account Managers increase revenue by $20\%$ month$-$over$-$month for accounts they manage up to a cap of $6$ months. To be clear, this revenue increase compounds by $20\%$ each month up to the $6$th month, at which point it maxes out and remains flat for the remaining duration of time that the customer has an account manager $($for example, if a customer has an account manager in month $1$ they$$ll pay $$120,$ in month $2$ they$$ll pay $$144,$ etc$).$ If a customer has an account manager and then loses the account manager their metrics $($revenue per month$)$ return to the baseline, but there isn$$t a negative consequence. Each Account Manager can carry $25$ customers. Each support agent increases CSAT by $1$ percentage point. Each point of CSAT leads to a $15\%$ relative decrease in churn.

SaaSafras needs you to make $3$ key decisions: $$ How many people will work on acquiring new business, account management, and support each month from month $1$ to month $24?$ Why are they working there? $$ We care about your understanding of the why behind your decisions just as much as we care about the actual decision, so please explain your reasoning, not just the conclusion $($i$.$e$.$ don$$t rely too much on solver $/$ other tools$).$ Bonus: If you had a magic wand, what is the one variable you would try to improve going into year $3?$ How would you approach moving that variable? $$ By $$variable$$ here, we mean one of your team members core metrics $($customer acquisition, CSAT, revenue increase, relative churn decrease etc$).$

Can you mathematical detail the answer