In order to maximize profit, attomey's should offer more services towardsGeneral law practices in smaller towns, like Phillip A$.$ Terwilliger in Vermillion, SD$,$ offer many different types of services. Depending on the type of service a person requires, the fees associated will vary as the time spent varies. Suppose a law firm, similar to Terwilliger's, offers the following services: Incorporation Paperwork for Small Businesses and Non$-$Profits, Estate Planning$/$Last Will and Testament, Probate Administration, and Civil Litigation. At the firm, the work has historically been done by the attorney, but paralegals can be contracted to assist. Contracting with paralegals is being considered to increase the amount of work the firm can complete; this would involve restructuring the work to be completed by both the attorney and a paralegal with the specialization needed for each service.

The firm charges clients $$200$ an hour for each attorney hour, $$100$ an hour for each paralegal hour, and each of the services has a typical number of hours it would take to complete the service. To ensure the attorney has time to spend with family, the attorney cannot work more than $160$ hours each month. To contract with each paralegal for the month, the attorney pays the paralegal a monthly fee plus an hourly rate for their time; these fees and rates vary by specialization. Paralegals have a limited number of hours they are available for each month and if a paralegal is not contracted for the service, the attorney would not be able to offer that service. This information is summarized below.

Incorporation Estate$/$Will Probate Civil Litigation

Attorney Hours $531030$

Paralegal Hours $862525$

Paralegal Monthly Fee $$600$ $$400$ $$600$ $$1000$

Paralegal Hourly Rate $$40$ $$45$ $$50$ $$60$

Paralegal Hours Available $303075100$

Assuming services cannot be offered in part, what services should the attorney offer to maximize profits? The optimal ourcome should be $$38,510($if your Optimality is set to $1)$ or $$38,540($if your Optimality is set to $0).$

NOTE: The paralegals are the focus for the decision variables and fixed charge apsects of this problem. The attorney only needs to stay under the total hourly constraint for the month; the attorney's workload will be dictated by what paralegals are hired.

Suppose the attorney is considering what happens in months when they work less hours because of holidays or more hours because of additional free time. What happens to services offered and profits when the number of hours the attorney is availble to work changes? $($Think about what type of changes make sense in this context.$)$