Question

In problems 1-2, notice that the linear programming problems given are not in standard form. (a) Change it into the standard form and write in matrix form, (b) convert it to canonical form and express this form in matrix notation. 1. Maximize $z = 2x + 5y$ subject to $3x + 2y \le 6$ $2x + 9y \le 8$ $x \ge 0$. 2. Maximize $z = 2x_1 + 3x_2 + 4x_3$ subject to $3x_1 + 2x_2 - 3x_3 \le 4$ $2x_1 + 3x_2 + 2x_3 \le 6$ $3x_1 - x_2 + 2x_3 \ge -8$ $x_1 \ge 0, x_2 \ge 0, x_3 \ge 0.$

          In problems 1-2, notice that the linear programming problems given are not in standard form.
(a) Change it into the standard form and write in matrix form, (b) convert it to canonical form
and express this form in matrix notation.
1. Maximize $z = 2x + 5y$ subject to
$3x + 2y \le 6$
$2x + 9y \le 8$
$x \ge 0$.
2. Maximize $z = 2x_1 + 3x_2 + 4x_3$ subject to
$3x_1 + 2x_2 - 3x_3 \le 4$
$2x_1 + 3x_2 + 2x_3 \le 6$
$3x_1 - x_2 + 2x_3 \ge -8$
$x_1 \ge 0, x_2 \ge 0, x_3 \ge 0.$

In problems 1-2, notice that the linear programming problems given are not in standard form.
(a) Change it into the standard form and write in matrix form, (b) convert it to canonical form
and express this form in matrix notation.
1. Maximize z = 2x + 5y subject to
3x + 2y ≤ 6
2x + 9y ≤ 8
x ≥ 0.
2. Maximize z = 2x1 + 3x2 + 4x3 subject to
3x1 + 2x2 - 3x3 ≤ 4
2x1 + 3x2 + 2x3 ≤ 6
3x1 - x2 + 2x3 ≥ -8
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

Added by Emily M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Matthew Wagner

Step 1

Maximize z = 2x + 5y subject to 3x + 2y ≤ 6 2x + 9y ≤ 8 x ≥ 0 y ≥ 0 (a) Standard form: Maximize z = 2x + 5y subject to 3x + 2y + s1 = 6 2x + 9y + s2 = 8 x, y, s1, s2 ≥ 0 Matrix form: Objective function: [2, 5, 0, 0] Constraints: [[3, 2, 1, 0], [2, 9, 0, Show more…

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In problems 1-2, notice that the linear programming problems given are not in standard form. (a) Change them into standard form and write them in matrix form. (b) Convert them to canonical form and express this form in matrix notation. Maximize 2 = 21 + 5y subject to 3r + 2y < 6, 2r + 9y < 8, I > 0. 2. Corrected_text: Maximize 2 = 2T1 + 3T2 + 4Ts subject to 3T1 + 2T2 - 313 < 4, 2T1 + 372 - 2T3 < 6, 311T2 + 213 - 2T8T1 > 0, T2 > 0, T3 > 0. Title_with_topic: Linear Programming Problems in Standard and Canonical Form