This is a problem is advange engineering mathematics A law f

This is a problem is advange engineering mathematics

A law firm handles two types of lawsuits: medical malpractice suits and wrongful termination suits. Each malpractice lawsuit requires 6 months of preparation and the hiring of 5 expert witnesses, whereas each termination lawsuit requires 10 months of preparation and 3 expert witnesses. The firm has a total of 30 months to work with and estimates that it cannot afford to hire more than 15 expert witnesses. The firm makes an average profit of $10, 000 per doctor sued and $50, 000 per employer sued. How many of each type of lawsuit should the firm initiate in order to maximize profit?

Solution

The law firms cases selection is based on two parameters: one being the duration of case completion and the witness hired. This leads us to two simultaneous linear eqn as follows,

To denote duration:

6 x + 10 y = 30 ----- eqn 1 which shows combination of duration in 30 months time

To denote hires:

5 x + 3 y = 15 -------- eqn 2 which shows combination of hires in 30 months time

To maximize profit it should be the result of a perfect combination of projects which reflects in the values of X and Y.

Solving eqn 1 and 2 and eliminating x we get,

44 x = 120, and x = 2 apprximately.

Now, y = 1 approximately

The profit maximizes when the 2 doctors and 1 employee is sued in 30 months time.