This is a problem is advange engineering mathematics A law firm handles two type

Question

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?

Explanation / Answer

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.

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