Answer:
The maximum revenue for the week is $19,000.
Step-by-step explanation:
Denote the variables as follows:
<em>X</em> = small business audit
<em>Y</em> = tax return
The maximizing function is:
<em>Z</em> = 2000·<em>X</em> + 300·<em>Y</em>
The maximizing function is subjected to the constraints:
100·<em>X</em> + 10·<em>Y </em>≤ 900
10·<em>X</em> + 2·<em>Y</em> ≤ 100
0 ≤ <em>X</em> and 0 ≤ <em>Y</em>
The problem can be solved using the simples method as follows:
Let <em>s</em> and <em>t</em> be slack variables.
Initial:
x y s t b Basic
<u>100</u> 10 1 0 900 s (departing)
12.5 2.5 0 1 100 t
<em>Z</em> -2000 -300 0 0 0
(entering)
Step 1:
x y s t b Basic
1 1/10 1/100 0 9 x
0 1 -1/10 1 10 t (departing)
<em>Z</em> 0 -100 20 0 18000
(entering)
Step 2:
x y s t b Basic
1 0 1/50 -1/10 8 x
0 1 -1/10 1 10 y
<em>Z</em> 0 0 10 100 19000
(entering)
The optimal solution is:
<em>X</em> = 8
<em>Y</em> = 10
The maximum revenue for the week is $19,000.
