A Mississippi farmer is considering producing a special kind of $0.25 \%$ fat milk. The potential buyer demands a minimum lot size of 1000 gallons. Let $X_{1}=$ represent the gallons of $0.25 \%$ milk produced. Let $\mathrm{Y}_{1}$ be a 0 or 1 variable; if it is 0 , it signifies that the $0.25 \%$ milk was not produced at all. If it is 1 , it signifies that 1000 or more gallons of $0.25 \%$ milk was produced. The constraint/s that implements this would be ( $\mathrm{M}$ stands for a very big positive number and assume non-negative variables.)
A) $X_{1} \geq 1000$
B) $\mathrm{X}_{1} \geq 1000 \mathrm{Y}_{1}$
C) $X_{1} \geq 1000+M^{*} Y_{1}$
D) $X_{1} \geq 1000+M^{*}\left(1-Y_{1}\right)$

Question

Quizplus · Accepted Answer

B) $X_{1} \geq 1000 Y_{1}$ correctly implements the constraint. If $Y_{1} = 0$, then $X_{1} \geq 0$, allowing for no production. If $Y_{1} = 1$, then $X_{1} \geq 1000$, ensuring the minimum production requirement is met.

A Mississippi Farmer Is Considering Producing a Special Kind Of 0.25