# Figure A-3

Determination of the basic feasible solution point

The leaving variable is determined by dividing the quantity values by the pivot column values and selecting the minimum possible value or zero.

The Simplex Method

A-11

the labor to make mugs (because no bowls are to be produced, x_{1 }= 0; and because we will use all the labor possible and s_{1 }= unused labor resources, s_{1 }= 0 also):

1 ( 0 ) + 2 x 2 + 0 = 4 0 1 x 1 + 2 x 2 + s 1 = 4 0 h r .

40 hr. x_{2 }= 2 hr>mug

= 20 mugs

In other words, enough labor is available to produce 20 mugs. Next, perform the same analysis on the constraint for clay:

4 ( 0 ) + 3 x 2 + 0 = 1 2 0 4 x 1 + 3 x 2 + s 2 = 1 2 0 l b .

120 lb. x_{2 }= 3 lb>mug

= 40 mugs

This indicates that there is enough clay to produce 40 mugs. But there is enough labor to pro- duce only 20 mugs. We are limited to the production of only 20 mugs because we do not have enough labor to produce any more than that. This analysis is shown graphically in Figure A-3.

x_{2 }

40

R

30

$50 profit

20

A

10

B

0

10

20 $40 profit

C 30

40

x_{1 }

Because we are moving out the x_{2 }axis, we can move from the origin to either point A or point R. We select point A because it is the most constrained and thus feasible, whereas point R is infeasible.

This analysis is performed in the simplex method by dividing the quantity values of the basic solution variables by the pivot column values. For this tableau,

1 2 Basic Variables s s

Quantity 40 120

x_{2 }, 2 = 20, the leaving basic variable , 3 = 40