9.3 THE SIMPLEX METHOD: MAXIMIZATION

506 CHAPTER 9 LINEAR PROGRAMMING
Now, to this initial tableau, we apply the simplex method as follows.
x1 x2 x3 s1 s2 s3 s4 b
Basic
Variables
3
1 10
20 20 0 0 0 10 x1 0 1 0 0 1 0 0 10 s2 ← Departing
0 0 1 0 s 3
37
10
7
10
0 0 0 1 s 4
0 10,000
↑
Entering
3,000 5,000 0 0 0 910,000
Basic
x 1 x 2 x 3 s 1 s 2 s 3 s 4 b Variables
1 0 0 0 x1 0 1 0 0 1 0 0 10 x2 0 0 1 0 s3 ← Departing
0 0 0 1
449
s4 37
20 20 10
10
23
20
1
20
7
10
161
10
47 9
0 0 3,000 5,000 10,000 0 0 1,010,000
↑
Entering
Basic
x 1 x 2 x 3 s 1 s 2 s 3 s 4 b Variables
1 0 0 0 4 x1 0 1 0 0 1 0 0 10 x2 0 0 1 0 14 x3 0 0 0 1 12 s4 0 0 0
118,000
23
272,000
23
60,000
23 0 1,052,000
From this tableau, we see that the maximum weekly audience for an advertising budget of
$18,200 is
47
23
118
23 23 23
1
23
14
23
20
23
8
23 23
z 1,052,000
3
20
3
23
20
47
20
Maximum weekly audience
and this occurs when x1 4, x2 10, and x3 14. We sum up the results here.
9
3
Media
Number of
Advertisements Cost Audience
Television 4 $ 8,000 400,000
Newspaper 10 $ 6,000 400,000
Radio 14 $ 4,200 252,000
Total 28 $18,200 1,052,000
1
1
20
9
20
1
20
1
3
10
91
91
10
819
10
61
10