To find: the numbers of audits and tax returns will yield an optimal revenue and the optimal revenue.
Answer to Problem 41E
Optimal revenue is 20800 and it is obtained when there is 13 audits and 0 tax returns.
Explanation of Solution
Given:
An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week. The firm charges $1600 for an audit and $250 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.
Calculation:
Let
The three constraints can be converted into linear inequalities as:
Since the number of pieces produced cannot be negative, we can get two more constraints of
The area determined by the constraints are shown below:
The point of intersection of two lines A, should be found by solving the equation of two lines:
From equation (1),
From equation (2),
At the intersection point
So the co-ordinates of the intersection point A is
At the four vertices of the region formed by the constraints the objective function has the following values:
At
At
At
At
Optimal revenue is 20800 and it is obtained when there is 13 audits and 0 tax returns.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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