2. 21 r³s⁶

3. z(z-4)(z+1)

4. (7k-9)/ k(k+3)(k-1)

5. (p+2m²) / m(4m+p)

6.  -m/( 2+m)

7. (a-2)/2a

8.  4(r-2)(r+2) / ( 5r+12) (r-1)

Hw 6.2   Q29

There are total of 15 steps.  I will only post those procedures since it will be too long to post the entire solution.

Pivot element: 1 fourth row and second colm.  Basic Var: S1,S2,S3,S4,P.

Step I:

5R₄ +R₅ ->  R₅

 Step II:

-4R₄ +R₃ -> R₃

Step III:

-3R₄ +R₂ ->R₂ 

Step IV:

-2R₄ +R₁ ->R₁   

Second Pivot:

Pivot Element: 1 first col and third row.  Basic element: S1,S2,S3, X2,P.

Step V:

-R₃ +R₁->R₁

Step VI:

-R₃ +R₂ ->R₂

Step VII:

2R₃ +R₅ ->R₅

Third Pivot:

Pivot element: 1 sixth colm and second row.  Basic var: S1,S2,X1,X2,P.

Step VIII:

-2R₂ +R₁ -> R₁

Step IX:

4R₂ +R₃ ->R₃

Step X:

-R₂ +R₄ ->R₄

Step XI:

3R₂ + R₅ -> R₅

 Fourth Pivot:

Pivot element: 1, fifth col and first row.

Basic Var: S3,S4,X1,X2, P.

Step XII:

R₁ + R₂ ->R₂

 Step XIII:

3R₁ +R₃ -> R₃

Step XIV:

-R₁ + R₄ ->R₄

Step XV:

R1+ R5 -> R5.

Then set: S1=0 and S2=0.

Solve the following with the above conditions:

S₁ - 2S₂ + S₃  =4

S₁ + S₄ =6

X₁ +3S₁ =24

X₂ - S₁ =8

S₁  + S₂ + P = 88

Chapter 5 overview:

1. Be familiar with various method of graphing lines previously discussed in chapter 4.
2. Graphing inequalities involved shading of the region.
3. Use the (0,0) testing point to determine the area to be shade
4. Know how to determine the corner points
5. What do bounded and unbounded mean?
6. What is the maximization problem?
7. What is the basic feasible region of solution?
8. How to determine the optimal solution? Another word, how to compute for P?

Chapter 6

1. How to determine the basic variables, non-basic variables?
2. What is the role of slack variables?  Think of the types of solution for the system we have solved from chapter 4.
3. Again, be familiar with the basic feasible solution
4. How to transform the standard maximization problems into the simplex tableau?
5. Know the process of pivoting, once the standard maximization problems is transform into the simplex tableau, determine the pivot column, pivot row, pivot element.
6. What is the goal of pivoting? To solve for:....................
7. How do you determine the basic variable on the left side of the simplex tableau?
8. When do you have the no solution case?  Note the schemata of pivoting.

God speed.