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 least 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 least 30 . The constraint/s that implements this would be (M stands for a very big positive number and assume non-negative variable)
A) $X_{2}+X_{3} \geq 50+M^{*}\left(1-X_{1}\right)$ and $2 X_{2}-3 X_{3} \geq 30+M^{*} X_{1}$
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) $X_{2}+X_{3} \leq 50+M^{*} X_{1}$ and $2 X_{2}-3 X_{3} \leq 30+M^{*}\left(1-X_{1}\right)$

Question

Quizplus · Accepted Answer

The correct constraints are $X_{2}+X_{3} \geq 50 X_{1}$ for when the bull is purchased, ensuring the sum of soy and corn is at least 50 if $X_{1}=1$, and $2 X_{2}-3 X_{3} \geq 30(1-X_{1})$ for when the bull is not purchased, ensuring the specified condition is met if $X_{1}=0$. This setup uses $X_{1}$ as a switch to activate the appropriate constraint.

A Mississippi Farmer Is Considering Adding a Special Breed of Bull