Consider a Mathematical Program Where X_i Represents the Amount Produced

Multiple Choice

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