Which of the following statements is correct?

  • A
    Every $LP$ problem has at least one optimal solution.
  • B
    Every $LP$ problem has a unique optimal solution.
  • C
    If an $LP$ problem has two optimal solutions,then it has infinitely many solutions.
  • D
    If a feasible region is unbounded then $LP$ problem has no solution.

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$x \leq 3, y \leq 2, x \geq 0, y \geq 0$

In solving the $LP$ problem: "Minimize $z = 6x + 10y$ subject to $x \geq 6, y \geq 2, 2x + y \geq 10, x \geq 0, y \geq 0$." The redundant constraints are $....$

If the vertices of a feasible region are $O(0,0), A(10,0), B(0,20), C(15,15)$,then the minimum value of the objective function $Z = 10x - 20y + 30$ is . . . . . . .

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