An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week.The firm charges $1700 for an audit and $410 for a tax return.Each audit requires 60 hours of staff time and 16 hours of review time.Each tax return requires 10 hours of staff time and 4 hours of review time.What numbers of audits and tax returns will yield an optimal revenue? What is the optimal revenue?
A)0 audit 65 tax returns
Optimal revenue: $6,560
B)5 audits 48 tax return
Optimal revenue: $28,180
C)16 audits 0 tax return
Optimal revenue: $27,200
D)10 audits 10 tax returns
Optimal revenue: $21,100
E)13 audit 0 tax returns
Optimal revenue: $28,180

Question

An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week.The firm charges $1700 for an audit and $410 for a tax return.Each audit requires 60 hours of staff time and 16 hours of review time.Each tax return requires 10 hours of staff time and 4 hours of review time.What numbers of audits and tax returns will yield an optimal revenue? What is the optimal revenue? ​
A)0 audit 65 tax returns
Optimal revenue: $6,560
B)5 audits 48 tax return
Optimal revenue: $28,180
C)16 audits 0 tax return
Optimal revenue: $27,200
D)10 audits 10 tax returns
Optimal revenue: $21,100
E)13 audit 0 tax returns
Optimal revenue: $28,180

Quizplus · Accepted Answer

We can set up the following linear programming model:

Maximize: 1700A + 410T
Subject to: 
60A + 10T <= 780 (staff time constraint)
16A + 4T <= 272 (review time constraint)
A, T >= 0 (non-negativity constraint)

Using a linear programming solver, we find that the optimal solution is A=5 and T=48, with an optimal revenue of $28,180. Therefore, the best choice is B.

An Accounting Firm Has 780 Hours of Staff Time and 272