Consider a mathematical program where X_i represents the amount produced of item i (i = 1,2,3,4), and you want the total amount produced over all four items to equal either 100, 120, 140, or 200. If you define q_i as binary (0-1) variables (i = 1,2,3,4) and add the constraint q₁ + q₂ + q₃ + q₄ = 1, what other constraint do you need to add to the program? A) 100q₁ + 120q₂ + 140q₃ + 200q₄ =560 B) X₁+ X₂ + X₃ + X₄ =560 C) X₁+ X₂ + X₃ + X₄ = 100q₁ + 120q₂ + 140q₃ + 200q₄ D) 100X₁+ 120X₂ + 140X₃ + 200X₄ = q₁ + q₂ + q₃ + q₄ E) X₁+ X₂ + X₃ + X₄ ≤ 200

Question

Quizplus · Accepted Answer

The given constraint ensures that only one of the binary variables q_i can take the value of 1, indicating which total amount is being produced. However, another constraint is needed to ensure that the sum of the amounts produced of each item i corresponds to the chosen total amount. This can be achieved with the constraint in choice C, which sets the left-hand side (LHS) of the equation to be the total amount produced, given the binary variable values, and the right-hand side (RHS) to be the chosen total amount, determined by the binary variable that takes the value of 1.

Consider a Mathematical Program Where Xi Represents the Amount Produced

Consider a Mathematical Program Where X_i Represents the Amount Produced