#7B

The Simplex method, PART 2

Example:

Beaver Creek Pottery Company

Exercise

a) When one bowl is produced, how much labor slack is used?

b) When one bowl is produced, how much clay slack will be used?

c) When one mug is produced, how much labor slack is used?

d) When one mug is produced, how much clay slack is used?

e) Represent these values in the objective function.

Recall (from handout 7A):

The entering variable: We chose X2 because it provides more profit (\$50). This is the highest positive value in the Cj – Zj row.

The leaving variable: We choose S1 as the leaving variable.

We want to produce mugs (the entering variable).

a) How many mugs can be produced with our 40 hours of labor?

b) How many mugs can be produced with our 120 pounds of clay?

Simplex Tableau for this Model

2nd Iteration

 Cj Basic Variables Quantity (RHS) Zj Cj - Zj

The various rows are computed using several simplex functions.

New pivot row values

new pivot row values = old pivot row values / pivot number

Quantity: 40 / 2 = 20

X1: 1 / 2 = ½

X2:

S1:

S2:

Remaining rows

(In this case, there is only one remaining row.)

new row values = old row values -

(corresponding coefficients in pivot column * corresponding new tableau pivot row value)

Quantity: 120 - (3 * 20) = 60

X1: 4 - (3 * ½) = 5/2 (or 2.5)

X2:

S1:

S2:

Zj row

These values will be computed in the same way they were in the first iteration (see handout 7A).

Quantity = (50 * 20) + (0 * 60) = 1000

X1: = (50 * ½) + (0 * 5/2) = 25

X2:

S1:

S2:

Cj – Zj row

These values will be computed in the same way they were in the first iteration (see handout 7A).

What is the entering variable?

What is the leaving variable?

Exercise:

Simplex Tableau for this Model

3rd Iteration

 Cj Basic Variables Quantity (RHS) Zj Cj - Zj