A company is planning next month's production. It has to pay a setup cost to produce a batch of X₄'s so if it does produce a batch it wants to produce at least 100 units. Which of the following pairs of constraints show the relationship(s) between the setup variable Y₄ and the production quantity variable X₄? A)X₄ $\ge$M₄Y₄, X₄ $\ge$ 100 B)X₄ $\le$M₄Y₄, X₄ = 100 Y₄ C)X₄ $\le$M₄Y₄, X₄ $\ge$ 100 Y₄ D)X₄ $\le$M₄Y₄, X₄ $\le$ 100 Y₄

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Quizplus · Accepted Answer

The constraint X₄ F1F1F1S1 ≤ F1F1F10 M₄Y₄ means that if a batch is produced (Y₄ = 1), then X₄ must be greater than or equal to 100. This makes sense as the company wants to produce at least 100 units if it incurs the setup cost. The constraint X₄ F1F1F1S1 ≥ F1F1F10 100 Y₄ means that if Y₄ = 0 (i.e., no batch is produced), then X₄ must be less than or equal to 100. This also makes sense as there is no need to incur the setup cost if the production quantity is less than 100. Therefore, choice C is the best choice as it includes both of these logical constraints.

A Company Is Planning Next Month's Production ≥\ge≥ M4Y4, X4 ≥\ge≥ 100 B)X4

A Company Is Planning Next Month's Production $\ge$ M₄Y₄, X₄ $\ge$ 100
B)X₄