Linear Programming

1. A.
   $2x + y \ge 2,\ x - y \ge 1,\ x + 2y \le 8,\ x \ge 0,\ y \ge 0$
2. B.
   $x + 2y \ge 2,\ x - y \ge 1,\ x + 2y \le 8,\ x \ge 0,\ y \ge 0$
3. C.
   $2x + y \ge 2,\ x - y \le 1,\ x + 2y \le 8,\ x \ge 0,\ y \ge 0$
4. D.
   $2x + y \ge 2,\ x - y \le 1,\ 2x + y \le 8,\ x \ge 0,\ y \ge 0$

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1. A.
   $17$
2. B.
   $18$
3. C.
   $35$
4. D.
   $53$

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1. A.
   a finite number of optimal solutions
2. B.
   a unique optimal solution
3. C.
   infinite number of optimal solutions
4. D.
   no feasible solution

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1. A.
   Graph A
2. B.
   Graph B
3. C.
   Graph C
4. D.
   Graph D

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1. A.
   $90$ and $190$
2. B.
   $60$ and $180$
3. C.
   $30$ and $120$
4. D.
   $40$ and $220$

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1. A.
   7250
2. B.
   9250
3. C.
   4250
4. D.
   5750

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1. A.
   $320$
2. B.
   $450$
3. C.
   $254$
4. D.
   $180$

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1. A.
   $(0, 0)$
2. B.
   $(1.5, 1.5)$
3. C.
   $(2, 0)$
4. D.
   $(0, 2)$

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1. A.
   a convex bounded region with 4 corner points
2. B.
   an unbounded region
3. C.
   a convex bounded region with 5 corner points
4. D.
   no feasible region

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1. A.
   maximize $z = 2x + 5y$ subject to $2x + y \le 360, 4x + 2y \le 120, x \ge 0, y \ge 0$
2. B.
   maximize $z = 2x + 5y$ subject to $2x + y \le 120, 4x + 2y \le 360, x \ge 0, y \ge 0$
3. C.
   maximize $z = 2x + 5y$ subject to $2x + 4y \le 360, x + 2y \le 120, x \ge 0, y \ge 0$
4. D.
   maximize $z = 2x + 5y$ subject to $2x + 4y \le 120, x + 2y \le 360, x \ge 0, y \ge 0$

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