The following partial initial simplex tableau is given:
|
Basis cB
|
x1
|
x2
|
x3
|
s1
|
s2
|
s3
|
|
|
5
|
20
|
25
|
0
|
0
|
0
|
|
|
2
|
1
|
0
|
1
|
0
|
0
|
40
|
|
0
|
2
|
1
|
0
|
1
|
0
|
30
|
|
3
|
0
|
-¹⁄2
|
0
|
0
|
1
|
15
|
|
zj
cj - zj
|
|
a. Complete the initial tableau.
b. Write the problem in tableau form.
c. What is the initial basis? Does this basis correspond to the origin? Explain.
d. What is the value of the objective function at this initial solution?
e. For the next iteration, which variable should enter the basis, and which variable should leave the basis?
f. How many units of the entering variable will be in the next solution? Before making this first iteration, what do you think will be the value of the objective function after the first iteration?
g. Find the optimal solution using the simplex method.