A Mississippi Farmer Is Considering Adding a Special Breed of Bull

Multiple Choice

A Mississippi farmer is considering adding a special breed of bull to his farm. Let $X_{1}=1$ imply that the bull will be purchased and 0 otherwise. If it is purchased, then the pounds of organic soy purchased per day (denoted by $\mathrm{X}_{2}$ ) and the pounds of organic corn purchased per day (denoted by $\mathrm{X}_{3}$ ) should be at most 50. If the bull is not purchased, then $2 *$ the pounds of organic soy purchased $-3^{*}$ the pounds of organic corn purchased should be at most 30. The constraint/s that implements this would be (M stands for a very big positive number and assume non-negative variables)

A) $X_{2}+X_{3} \geq 50+M^{*} X_{1}$ and $2 X_{2}-3 X_{3} \geq 30+M^{*}\left(1-X_{1}\right)$
B) $X_{2}+X_{3} \geq 50 X_{1}$ and $2 X_{2}-3 X_{3} \geq 30\left(1-X_{1}\right)$
C) $X_{2}+X_{3} \leq 50 * X_{1}$ and $2 X_{2}-3 X_{3} \leq 30\left(1-X_{1}\right)$
D) $X_{2}+X_{3} \leq 50+M^{*}\left(1-X_{1}\right)$ and $2 X_{2}-3 X_{3} \leq 30+M^{*} X_{1}$