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Table A-10

Computation of the New Pivot Row Values

c j

50 0

Basic Variables

x s2 2

Quantity

20

40

50

0

0

x1

x2

s1

s2

1/2

1

1/2

0

The Simplex Method

A-13

z j

c j - z j

new tableau row values

=

old tableau row values

  • -

    £

corresponding coefficients in pivot column

*

corresponding new tableau pivot row value

Thus, this formula requires the use of both the old tableau and the new one. The s2 row val- ues are computed in Table A-11.

120

-

(3

*

20)

=

60

4

-

(3

*

1/2)

=

5/2

3

-

(3

*

1)

=

0

0

-

(3

*

1/2)

=

-3>2

1

-

(3

*

0)

=

1

These values have been inserted in the simplex tableau in Table A-12. This solution corresponds to point A in the graph of this model in Figure A-3. The solu- tion at this point is x1 = 0, x2 = 20, s1 = 0, s2 = 60. In other words, 20 mugs are produced and 60 pounds of clay are left unused. No bowls are produced and no labor hours remain unused.

Quantity x x s s 1 2 1 2

£ Corresponding Coefficients in Pivot Column

*

New Tableau Pivot Row Value

=

New Tableau Row Value

Table A-11

Computation of New s2 Row Values

Column

Old Tableau Row Value

-

Table A-12

The Second Simplex Tableau with Row Values

c j

50 0

Basic Variables

x s2 2

40

50

0

0

Quantity

x1

x2

s1

s2

20

1/2

1

1/2

0

60

5/2

0

-3/2

1

z j

c j - z j

T h e s e c o n d s i m p l e x t a b l e a u i s c o m p l e t e d b y c o m p u t i n g t h e a n d r o w v a l u e s t h e s a m e w a y t h e y w e r e c o m p u t e d i n t h e f i r s t t a b l e a u . T h e r o w i s c o m p u t e d b y s u m m i n g t h e p r o d u c t s o f t h e c o l u m n a n d a l l o t h e r c o l u m n v a l u e s . c j z j c j - z j z j

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