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(B) We are given the objective function: Maximize $z = 4x_1 + 2x_2$.Subject to the constraints:$1) 3x_1 + 2x_2 \geq 9$$2) x_1 - x_2 \leq 3$$3) x_1 \ge

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Unbounded solution

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(B) We are given the objective function: Maximize $z = 4x_1 + 2x_2$.Subject to the constraints:$1) 3x_1 + 2x_2 \geq 9$$2) x_1 - x_2 \leq 3$$3) x_1 \geq 0, x_2 \geq 0$By plotting these lines on the coordinate plane:For $3x_1 + 2x_2 = 9$,the intercepts are $(3, 0)$ and $(0, 4.5)$. The region is away from the origin.For $x_1 - x_2 = 3$,the intercepts are $(3, 0)$ and $(0, -3)$. The region is towards the origin.Upon analyzing the feasible region,we observe that the region is unbounded in the first quadrant. For an unbounded feasible region,if the objective function increases indefinitely as we move along the boundary,the $L$.$P$.$P$. has an unbounded solution. Here,as $x_1$ and $x_2$ increase,$z = 4x_1 + 2x_2$ can take arbitrarily large values within the feasible region. Therefore,the $L$.$P$.$P$. has an unbounded solution.

For the Linear Programming Problem ($L$.$P$.$P$.),maximize $z = 4x_1 + 2x_2$ subject to the constraints $3x_1 + 2x_2 \geq 9$,$x_1 - x_2 \leq 3$,$x_1 \geq 0$,$x_2 \geq 0$,the problem has:

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