Help with Optimization of functions of n-variables!

Hi, I'm not sure what to use for a formula for this question. Any help is greatly appreciated :)

An accounting firm uses partners and staff to produce an audit. The quality of

the audit (as measured by reduction in litigation liability and the likelihood of

audit errors) is a function of the composition of the audit team. In particular

where r is the audit quality, P is the partner-hours devoted to the audit, and S

is the staff hours devoted to the audit. Notice that both partners and staff are

essential for the audit quality, and that audit quality increases in the amount

of either, but at a decreasing rate. The cost of a partner hour is 100 while

the cost of a staff hour is 20. The budget for this audit is 3000. How many

partner and staff hours will the accounting firm choose to maximize quality

subject to this budget constraint?

Re: Help with Optimization of functions of n-variables!

That is somehow an amazing solution Dinky, I think that formula will surely work to solve Sean's problem.

"I hate litigation support problems."