A company will be able to obtain a quantity discount on component parts for its three products, X₁, X₂ and X₃ if it produces beyond certain limits. To get the X₁ discount it must produce more than 50 X₁'s. It must produce more than 60 X₂'s for the X₂ discount and 70 X₃'s for the X₃ discount. Which of the following pair of constraints enforces the quantity discount relationship on X₃? A) X₃₁ ≤ M₃Y₃, X₃₂ ≥ 50Y₃ B) X₃₁ ≤ M₃Y₃, X₃₁ ≥ 50 C) X₃₂ ≥ (1/50)X₃₁, X₃₁ ≤ 50 D) X₃₂ ≤ M₃Y₃, X₃₁ ≥ 50Y₃

Question

Quizplus · Accepted Answer

The constraints in choice D follow the same pattern as the constraints given for X₁ and X₂. The first constraint states that the quantity produced of X₃ must be less than or equal to the maximum quantity available for the discount, which is determined by the production level multiplied by the discount rate. The second constraint states that the quantity produced of X₃ must be greater than or equal to the minimum production level required for the discount. Therefore, choice D is the best choice for enforcing the quantity discount relationship on X₃.

A Company Will Be Able to Obtain a Quantity Discount