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Table Method HW 10 Maximize $P = 10x_1 + 25x_2$ Subject to: $3x_1 + 2x_2 \le 21$ $x_1 + 5x_2 \le 20$ and the nonnegative constraints. There will be two slack variables here (see below) Build a table of \"basic solutions\" This table will have spaces for each decision variable and slack variable (one column each) plus an extra column for the P function $x_1$ $x_2$ $s_1$ $s_2$ 0 0 0 0 0 0 0 0 0 0 0 0 It will have as many rows as needed to have all combinations of two zeros in each row. Now write the e-system (the one where you put a slack variable in each constraint to take up the slack. $3x_1 + 2x_2 + s_1 = 21$ $x_1 + 5x_2 + s_2 = 20$ For each row, now put in the two zeros and solve for the two remaining unknowns First case, both x1 and y1 are zero. So, s1 is 21 and s2 is 20. Continue to do that for each row. Taking only the rows where all four variables are positive, plug the x's into the P equation, then chose the largest.

          Table Method HW 10
Maximize $P = 10x_1 + 25x_2$
Subject to:
$3x_1 + 2x_2 \le 21$
$x_1 + 5x_2 \le 20$
and the nonnegative constraints.
There will be two slack variables here (see below)
Build a table of \"basic solutions\" This table will have spaces for each decision variable and slack variable
(one column each) plus an extra column for the P function
$x_1$
$x_2$
$s_1$
$s_2$
0
0
0
0
0
0
0
0
0
0
0
0
It will have as many rows as needed to have all combinations of two zeros in each row.
Now write the e-system (the one where you put a slack variable in each constraint to take up the slack.
$3x_1 + 2x_2 + s_1 = 21$
$x_1 + 5x_2 + s_2 = 20$
For each row, now put in the two zeros and solve for the two remaining unknowns
First case, both x1 and y1 are zero. So, s1 is 21 and s2 is 20.
Continue to do that for each row.
Taking only the rows where all four variables are positive, plug the x's into the P equation, then chose
the largest.

Table Method HW 10
Maximize P = 10x1 + 25x2
Subject to:
3x1 + 2x2 ≤ 21
x1 + 5x2 ≤ 20
and the nonnegative constraints.
There will be two slack variables here (see below)
Build a table of b̈asic solutionsT̈his table will have spaces for each decision variable and slack variable
(one column each) plus an extra column for the P function
x1
x2
s1
s2
0
0
0
0
0
0
0
0
0
0
0
0
It will have as many rows as needed to have all combinations of two zeros in each row.
Now write the e-system (the one where you put a slack variable in each constraint to take up the slack.
3x1 + 2x2 + s1 = 21
x1 + 5x2 + s2 = 20
For each row, now put in the two zeros and solve for the two remaining unknowns
First case, both x1 and y1 are zero. So, s1 is 21 and s2 is 20.
Continue to do that for each row.
Taking only the rows where all four variables are positive, plug the x's into the P equation, then chose
the largest.

Added by Jonathan C.

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