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 audit quality, and that audit quality increases in the amount of either, but at a decreasing rate.
The cost of a partner-hour is 50 while the cost of a staff-hour is 5. The budget for this audit is 5000. How many partner and staff hours will the accounting firm choose to maximize quality subject to this budget constraint?
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