An accounting firm charges $2500 for an audit and $350 for a tax return.Research and available resources have indicated the following constraints. The firm has 900 hours of staff time available each week.
The firm has 155 hours of review time available each week.
Each audit requires 75 hours of staff time and 10 hours of review time.
Each tax return requires 12.5 hours of staff time and 2.5 hours of review time.
The accounting firm lowers its charge for an audit to $2000.What numbers of audits and tax returns will bring in an optimal revenue?
A) The optimal revenue will be $24,700 if the firms does 5 audits and 42 tax returns each week.
B) The optimal revenue will be $24,000 if the firms does 12 audits and 0 tax returns each week.
C) The optimal revenue will be $21,700 if the firms does 0 audits and 62 tax returns each week.
D) The optimal revenue will be $0 if the firms does 0 audits and 0 tax returns each week.
E) The optimal revenue will be $30,000 if the firms does 12 audits and 0 tax returns each week.

Question

Quizplus · Accepted Answer

To determine the optimal revenue, we need to use linear programming. Let x be the number of audits and y be the number of tax returns. The objective function is 2500x + 350y, which represents the total revenue. The constraints are:
75x + 12.5y ≤ 900 (available staff time)
10x + 2.5y ≤ 155 (available review time)
x ≥ 0 (non-negative number of audits)
y ≥ 0 (non-negative number of tax returns)

If the firm lowers its charge for an audit to $2000, the objective function becomes 2000x + 350y. Solving the linear programming problem using software or graphing, we obtain x = 5 and y = 42 as the optimal solution with total revenue of $24,700. Therefore, the best choice(s) is A.

An Accounting Firm Charges $2500 for an Audit and $350