Arthur and Son P.A. is an auditing firm that conducts both financial and operational audits. Arthur can conduct 90 financial audits (FAs) per year if he spends full time on just FAs or 180 operational audits (OAs) per year full time or any linear combination of both. (Note: a linear combination means that because the capacity required for 1 FA is the same as that for 2 OAs (90 to 180 ratio), Arthur can conduct such combinations as 89 FAs plus 2 OAs, or 88 FAs plus 4 OAs, and so on. Son processes the reports made by Arthur. Son can prepare 180 financial audit reports or 150 operational audit reports per year, or any linear combination thereof. The office staff finalizes the reports submitted by Son. They can handle no more than 160 reports of any kind, per year. Arthur and Son have calculated that to keep their association solvent, they must produce at least 30 FAs and 50 OAs each year. The profit from each FA has averaged $720 in the past and for each OA has been about $650. How may FAs and OAs should Arthur and Son attempt to conduct each year to maximize their firm's profits? Formulate as a linear program. Do not solve.
Arthur and Son P.A. is an auditing firm that conducts both financial and operational audits. Arthur can conduct 90 financial audits (FAs) per year if he spends full time on just FAs or 180 operational audits (OAs) per year full time or any linear combination of both. (Note: a linear combination means that because the capacity required for 1 FA is the same as that for 2 OAs (90 to 180 ratio), Arthur can conduct such combinations as 89 FAs plus 2 OAs, or 88 FAs plus 4 OAs, and so on. Son processes the reports made by Arthur. Son can prepare 180 financial audit reports or 150 operational audit reports per year, or any linear combination thereof. The office staff finalizes the reports submitted by Son. They can handle no more than 160 reports of any kind, per year. Arthur and Son have calculated that to keep their association solvent, they must produce at least 30 FAs and 50 OAs each year. The profit from each FA has averaged $720 in the past and for each OA has been about $650.
How may FAs and OAs should Arthur and Son attempt to conduct each year to maximize their firm's profits?
Formulate as a linear program. Do not solve.
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