x y s t P 1 -3 1 0 0 12 1 2 0 1 0 3 -6 -4 0 0 1 0 The pivot element for the init

Question

x y s t P

1 -3 1 0 0 12

1 2 0 1 0 3

-6 -4 0 0 1 0

The pivot element for the initial simplex tableau show is the red 1. So we need to zero out the other elements of column x. What is the formula used to zero out row 1 and column x?

Multiply Row _____by_______ and then

add the result to Row_____

What is the formula used to zero out row 3 column x?

Multiply Row _____by_______ and then

add the result to Row_____

Use your formulas to come up with the resulting table below:

x y s t P

a b c d e f

1 2 0 1 0 3

g h i j k l   

a=_______________ b=_______________ c=_______________

d=_______________ e=_______________ f=_______________

g=_______________ h=_______________ i=_______________

j=_______________ k=_______________ l=_______________

Question 5: 10 points

x y s t P

0 1 1/3 1/2 0 9

1 0 0 1 0 3

0 0 0 6 1 18

What is the conclusion derived the final simplex tableau shown?

The maximum profit is when x is

And y is .

Explanation / Answer

Given simplex tableau is :

1) Multiply Row __2___by___-1____ and then add the result to Row__1___.

2) Multiply Row __2___by___6____ and then add the result to Row___3__.

3) Given,

Now, the actual table is :

Then, a = 0, b = -5, c = 1, d = -1, e = 0, f = 9, g = 0, h = 8, i = 0, j = 6, k = 1, l = 18.

4) Given final simplex tableau :

From final table we conclude that the maximum profit is when x = 3 and y = 9.

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