For each system, determine if it is in standard form, or if it can be modified to be in standard form. The result would not just have to be in standard form; it also has to be equivalent to the original system.

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Maximize $$P = 8 x_1 + x_2 + 5 x_3$$ subject to the constraints

$$\begin{array}{rrrrrcr} x_1 & + & 7 x_2& + & 5 x_3 & \ge & -8 \cr x_1 & - & 9 x_2& & & \le & -7 \cr \end{array}$$
$$x_1\ge 0 \qquad x_2 \ge 0 \qquad x_{3} \ge 0$$

A. This can be put in standard form by replacing $x_1 - 9 x_2 \le -7$ with $x_1 + 9 x_2 \le 7$
B. This can be put in standard form by replacing $x_1 + 7 x_2 + 5 x_3 \ge -8$ with $-x_1 - 7 x_2 - 5 x_3 \le 8$
C. This can be put in standard form by both replacing $x_1 + 7 x_2 + 5 x_3 \ge -8$ with $-x_1 - 7 x_2 - 5 x_3 \le 8$ and replacing $x_1 - 9 x_2 \le -7$ with $x_1 + 9 x_2 \le 7$
D. This system is already in standard form
E. This system cannot be put in standard form

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Maximize $$P = 3 x_1 + 7 x_2$$ subject to the constraints

$$\begin{array}{rrrcr} -3 x_1 & + & 9 x_2 & \ge & -10 \cr 6 x_1 &- &x_2 &\le &3 \cr x_1\ge 0 &&x_2 & \ge & 0 \end{array}$$

A. This can be put in standard form by replacing $-3 x_1 + 9 x_2 \ge -10$ with $3 x_1 + 9 x_2 \le 10$
B. This can be put in standard form by replacing $-3 x_1 + 9 x_2 \ge -10$ with $3 x_1 - 9 x_2 \le 10$
C. This can be put in standard form by replacing $6 x_1 - x_2 \le 3$ with $6 x_1 + x_2 \le 3$
D. This system is already in standard form
E. This system cannot be put in standard form

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Maximize $$P = 6 x_1 + 4 x_2 + 6 x_3$$ subject to the constraints

$$\begin{array}{rrrrrcr} x_1 & - & x_2& + & 9 x_3 & \le & 3 \cr x_1 & - & x_2& & & \ge & 9 \cr && &&x_{3} & \le & 9 \end{array}$$
$$x_1\ge 0 \qquad x_2 \ge 0 \qquad x_{3} \ge 0$$

A. This can be put in standard form by replacing $x_1 - x_2 + 9 x_3 \le 3$ with $x_1 + x_2 + 9 x_3 \le 3$
B. This can be put in standard form by dropping $x_{3} \le 9$
C. This can be put in standard form by replacing $x_1 - x_2 \ge 9$ with $x_1 - x_2 \le 9$
D. This system is already in standard form
E. This system cannot be put in standard form

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Maximize $$P = x_1 + 5 x_2 + x_3$$ subject to the constraints

$$\begin{array}{rrrrrcr} 8 x_1 & - & 8 x_2& & & \ge & - 7 \cr -7 x_1 & + & x_2& - & x_3 & \le & 9 \end{array}$$
$$x_1\ge 0 \qquad x_2 \ge 0 \qquad x_{3} \ge 0$$

A. This can be put in standard form by replacing $-7 x_1 + x_2 - x_3 \le 9$ with $7 x_1 - x_2 + x_3 \ge -9$
B. This can be put in standard form by replacing $8 x_1 - 8 x_2 \ge - 7$ with $8 x_1 - 8 x_2 \le 7$
C. This can be put in standard form by replacing $8 x_1 - 8 x_2 \ge - 7$ with $-8 x_1 + 8 x_2 \le 7$
D. This system is already in standard form
E. This system cannot be put in standard form