Use the two-stage method to solve.
-Find $x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0$ such that
$$x_{1}+x_{2}+x_{3} \leq 125$$
$$x_{1}+x_{2}+x_{3} \geq 75$$
And $z=2 x_{1}+5 x_{2}+3 x_{3}$ is maximized.
A) $x_{1}=125, x_{2}=0, x_{3}=0, z=250$
B) $x_{1}=0, x_{2}=0, x_{3}=125, z=375$
C) $x_{2}=100, x_{3}=25, x_{1}=0, z=575$
D) $x_{2}=125, x_{1}=0, x_{3}=0, z=625$

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The Answer of Use the two-stage method to solve.
-Find $x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0$ such that
$$x_{1}+x_{2}+x_{3} \leq 125$$
$$x_{1}+x_{2}+x_{3} \geq 75$$
And $z=2 x_{1}+5 x_{2}+3 x_{3}$ is maximized.
A) $x_{1}=125, x_{2}=0, x_{3}=0, z=250$
B) $x_{1}=0, x_{2}=0, x_{3}=125, z=375$
C) $x_{2}=100, x_{3}=25, x_{1}=0, z=575$
D) $x_{2}=125, x_{1}=0, x_{3}=0, z=625$

Use the Two-Stage Method to Solve x1≥0,x2≥0,x3≥0x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0x1​≥0,x2​≥0,x3​≥0

Use the Two-Stage Method to Solve $x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0$